- きた is used to indicate physical movement here, like in 持ってきた
- In your examples, such movement verbals refer to a person, not the apartment
- It's not natural-sounding here to use a non-person after きた
- Without きた, the speaker and the apartment's locations could be separate
- Sentence modifiers restrict grammar/particles, enabling ambiguity
- Since 引っ越す can take a lot of particles, and it's a person that does the 引っ越す, it's still not that common, except in the middle of a sentence, to directly modify the 引っ越し先 with 引っ越す.
- If something is grammatical but overly ambiguous, find a different way to express it (e.g. 新しい引っ越し先)
- Particles like に can help disambiguate whether you mean the old or new apartment
- In this specific example, 引っ越す is better than 引っ越し
- For most words, no single stackexchange answer can illuminate every possible usage
- ここは 三月前に引っ越ししてきたアパートです。
- ここは 三月前に引っ越ししたアパートです。
I would like a detailed explanation about the use of "てきた" because I don't understand if it's here to add the nuance of action towards the speaker’s current location (like "本を持っきた") or to add a nuance of action that has been happening for something and extends to the present (like "その木は、芽が出てきた") .
First, as you'll see below, when your chosen way of expressing something turns out to be ambiguous, there's a good chance it's unnatural unless you change some things up. You could choose your words to avoid ambiguity by saying stuff like「この間引っ越したマンションは綺麗だな」, 「ここに3月前に引っ越してきました」,「あそこは前言っていた2月末に引っ越した新しい家です」,「新しく引っ越してきた隣人がうるさい」,「この間引っ越したアパートは汚かった」。You could talk about 前の家、前に住んでいた家、旧家、引っ越された先、この間出た家, etc., etc. But I won't really touch on other ways to use 引っ越す as a sentence modifier, or other ways to refer to a 引っ越し先・引っ越し元. There are just way too many ways you can express any given concept for me to go into. Don't worry about every theoretically possible grammar structure, don't obsess over searching for the most concise way to express everything, and conversely don't stress about every potential semantic ambiguity in a given utterance.
Second, in my experience, when expressing 引っ越し the way your example sentences do, I feel like it's more common to directly use the verbal itself, e.g. 引っ越してきた, rather than the derived compound verbal 引っ越し(を)する. If I were to attempt to describe the difference, I'd say that, generally, 引っ越し is more used when focusing on the act of moving itself, as in "okay, I'm going to move!"
Now, regarding your confusion about Enno Shiojiさん's answer (which I guess I could talk about in a comment):
The first sentence definitely sounds better, because "このアパート" implies
you are close to the apartment in question (so it's natural to say you
came to it via 引っ越し).
Let's say last week you signed a lease for a new apartment, but right now you're at work on your lunch break, and your new apartment is all the way across town. Now let's say you want to activate your utilities/the utility bill, so you make a phone call. On the phone, if you say このアパートには、三ヶ月前に引っ越してきました, since きました implies you came to the place mentioned, saying that would tell the person on the phone that you are probably in your apartment right now (STALKER ALERT!). But since you're actually somewhere else (at work), it might sound better to just say 引っ越しました。More on why below. Still, you're using この in both sentences here (or ここ in your original examples), so unless there's some other context, that will usually imply that the apartment and the speaker are in the same place. This brings us to the subject of agreement: since きた agrees with この, it's more natural to use きた here, especially because 引っ越してきた is a bit of a collocation.
Next, to your questions.
In this case, as you suggested, きた is used in the sense of coming to a location. In the case of 引っ越し it refers to a person. Therefore, when you use くる・いく as modifiers, it's most natural if they modify words like 私、人、彼女, etc.
引っ越す or 引っ越し refers to the act of moving. From 新明解国語辞典第五版:
(As of a couple months ago, Google translate has gotten pretty great IMO, if you want to translate these yourself. js)
In these definitions 移る[こと] and 変える are the keywords. Both of these words refer to changing something (the former, location, the latter, something in general), but depending on context and grammar they can be used to refer to moving/changing TO or moving/changing FROM. Note how in the first definition both から and に are used, and how in the second neither is used.
Perhaps even more key to your question, though, are the terms 住む家 and 住居. That is, 引っ越す as a concept refers to (when thinking about apartments, at least) when someone changes where they live. The location itself does not physically get up and move, nor does the person(!); rather, the place that the person designates to be where they live is what changes. If you know programming, it's like moving a pointer, with the pointer being, I guess, the person (or maybe the database information specifying their registered address). The person IS usually the one that does the 引っ越す (if we're talking about someone's house), but 引っ越す alone doesn't automatically contain the idea of くる or いく. The fact that that in English, "move" implies literal movement too doesn't help in understanding this subtlety.
Thus, you can say things like:
In other words, 引っ越した indicates that the act of moving [house] was performed; きました indicates that you have now come to where you are speaking. Abstractly speaking, 引っ越した doesn't care where the person is.
Your example sentences use no direction particle or verbal, though, making them ambiguous. You could say that the real "culprit" of the ambiguity here is the use of sentence modification, which as a grammatical structure is comparatively prone to creating ambiguity because only predicates can be strung together with it. Unless we start getting into 学校文法 territory and talking about how things like how た is actually a particle, basically the rub is that since you can't really predicate a sentence with a particle, sentence modification often implies no particle describing the modified nominal:
- ここは 三月前に引っ越ししてきたアパートです。
- ここは 三月前に引っ越ししたアパートです。
Since 引っ越し doesn't by itself specify location, the second sentence is ambiguous. Is this the old apartment you moved away from and are now standing by looking at nostalgically, or the apartment you moved to as your showing it off to your parents? Furthermore, where is the speaker located when making these statements? On the phone at work, or at the apartment in question? ここ can certainly (perhaps usually) imply that the speaker is presently at the apartment, but, depending on previous utterances, they don't absolutely HAVE to be. That's a bit beside the point, though. Plus, since the one who does the 引っ越す is still a person, while you can form countless acceptable utterances using 引っ越した to modify the 引っ越し先, it's definitely less common to just end the sentence right there. If you end the sentence with 引っ越した＋名詞+です, the 名詞 will probably be the person who moved (but not always).
Alright, so if the second sentence is ambiguous, what about the first sentence? Just like in 行ってきます and 持ってきてください, きた here specifies directionality/movement/location: the speaker CAME here having moved. Thus, when someone reads the first sentence, they can only conclude that you're talking about the apartment you moved to. But, just to be clear, in this situation, because it's a person that physically moves, it's not as natural to put アパート after きた.
One important thing to keep in mind is that the referent of the sentence, and where you are saying you are, can be different. Some other possible ways to indicate directionality when discussing 引っ越し：
- ここは三月前に引っ越していったアパートです。(いった: old apartment; unnatural)
- ここは三月前に引っ越したアパートです。(no direction, ambiguous; unnatural)
- このアパートには、三ヶ月前に引っ越してきました。(uses に+くる: new apartment)
- このアパートからは、三ヶ月前に引っ越しました。(uses から/no direction verbal: old)
- このアパートには、三ヶ月前に引っ越しました。(uses に: new)
- このアパートからは、三ヶ月前に引っ越してきた。(uses から: referent is old; but きた, so you're at the new one when you're saying this)
Strictly speaking, only the sentences that use くる or いく give away/imply the speaker's present location. Also notice how the first two sentences, which use sentence modification, don't include a に or から describing the apartment. It's not impossible to include particles in sentence modifiers, but some kinds of particles (I think に is actually the worst offender) often can't be well positioned to actually describe the modified word (被修飾語). And with a word like 引っ越す, where you might wonder about 誰が、どこから、どこに？, particles are pretty important. You could definitely say something like:
- ここは三月前に東京から引っ越してきたアパートです。(unnatural b/c not a person)
to clarify that you're talking about the new place. But note that から is referring to the old place.
Finally, you might be wondering if particle に could be used ambiguously here, since に can be used to indicate both from FROM where something came, and TO where it went, e.g.:
When indicating physical direction/location, に is unambiguous, so if you use it you'll always refer to the new place.
- Japanese is often concerned with the relationship between the speaker, the listener, and the referent of an utterance.
- Since the concept of 引っ越し doesn't refer to the present location of the speaker, but rather to that of his abode (the referent), a word like きた in its literal movement meaning can be used to separately clarify directionality/location of the speaker.
- Japanese as a grammar doesn't enjoy ambiguity, it only tolerates it
- Sentence modification often introduces ambiguity, by e.g. effectively restricting how you can use particles (especially に) with the modified word, and by moving words away from their referents; so in this case avoiding such a grammar structure also makes it easier to do stuff like use particles like に to specify physical location/direction. You could also add additional words for context, like 新しい.
- Words like ここ and この also, unless being used abstractly, frequently imply the location of the subject/focus/referent of the sentence. (Well, I guess in your examples ここ IS the subject (the topic), and アパート is the object, or whatever the English terms are.)
- Your second sentence could still be referring to the old place, since 引っ越し/引っ越す doesn't specify FROM vs TO by itself (i.e. without a particle like を、から、に, etc.) - although usually if you're talking about a specific location, it's assumed to be where you moved TO, unless から/を is explicitly used.
- Since you're focusing on where you moved to rather than the act of moving, 引っ越す is more natural than 引っ越し here.
- Because きた and ここ are in agreement, and ここ/引っ越し alone are slightly ambiguous, using きた here is more natural
- When 引っ越していく・きた, etc. modifies a nominal, that nominal (the 被修飾語) is usually a person, because it's a person that undertakes the physical movement, and placing related words close together is more natural (which is why modifying the 引っ越し先 with きた can be confusing)
- Unless made explicit with e.g. を、引っ越す/引っ越し is a general concept that needn't refer to a change in location of either a person or a home; only a change in where home of that person is located (e.g. この辺に引っ越してきた)
- Agreement, unambiguity, grammar, redundancy, and usage frequency can be used to determine which of two utterances is relatively more or less natural to say
- I went overboard here (don't ask how long this took to revise), and I'm pretty sure I said everything twice in this answer (even after removing extra details that might've been over your head). Someone feel free to edit for clarity/content