I'm not an expert in Japanese, but I am familiar with phonology.
Does "before" here mean in the past or it means to put [ɕ, t͡ɕ] before /i/, /s, t/.
It is definitely not referring to time here. It's the latter option, "put [those sounds] before [the other sounds]".
Also what's the point of grouping /s/ and /t/ inside a single pair of slashes /s, t/.
This is for the sake of convenience and brevity. In academic writing, if you can save some ink in one place, you can use more elsewhere, I guess.
And for the main question:
I'm very confused about the sound for ジ, is it [d͡ʑ] or [ʑ] followed by [i]?
The answer is in the Wikipedia article quotation, it seems. People will either always randomly choose one or the other (called "free variation"), or they always won't. That's not very helpful, unfortunately, because there is no way to distinguish them in writing.
One potential solution to this problem is to not worry about it by declaring yourself to be one of those "free variation" people. As a second language learner, this is probably the most prudent way, as there are more important questions to answer when it comes to your progress with the language. Time and experience with the language will help you decide which words people tend to use one or the other with, though.
The good news is that like Atsutane said, these sounds are allophones, so not knowing which one to say yourself won't impact your understanding of others because no words will be distinguished with just those sounds alone.
When geminated, however, /z/ is always [d͡z].
At least this is clear. If geminated ("making the consonant longer", as in with little っ), there's only one choice.
Note about phonemes and allophones
Phonemes are sound units that have meaning. That means if you have a word and swap one of the phonemes for another one, it will change the meaning of the word (or make a nonsense word). For example, in English, /b/ and /p/ are phonemes (sounds that mean something in English), and we know this because if we exchange them in a word, it changes the word, like this:
"Bat" /bæt/ becomes "pat" /pæt/
Note that phonemes are written between / / (forward slashes).
Likewise, if two sounds are allophones, they are two sounds that mean the same thing. Think of them as variations of a sound. If you exchange allophones within a word, it doesn't change the meaning. This is why we can have accents and still understand each other — we say different sounds but they mean the same thing. There are lots of examples, but take the word "butter" for example. Some people say the /t/ very clearly, but others will say it almost like a /d/, with a sound called a tap:
Butter /bʌtər/ and [bʌɾər]
Allophones are written between brackets [ ].
If I say both of these, an English speaker would only hear one word, "butter", even though I said two different sounds. There are tons more examples, especially with vowels, but in Japanese, there's one very famous example of allophones: [l] and [r]. To them, if you switch them out in a word, it sounds like the same word. This is why they have difficulty differentiating words like "light" and "right" when they learn English.