In my experience, once you get to this level it is sometimes easier to understand these intuitively because you can understand a lot from the context and the way the person says the phrase.
Breaking them down can get quite complicated because grammatically there is a lot going on: I have given two ways to analyse 〜たんじゃない but I think they both have merit.
My take on
"I wasn't the one who issued that threat, but no matter."
ー＞ Spoken Japanese, might even contain colloquialisms that seem contradictory just as they do in English ("I haven't eaten none of them.")
"but no matter..."
ー＞ Spoken English also leaves some things unsaid and that seems to be case here. I have not seen the film so I don't know what happens next or before but I guess you will understand from the context.
ー＞ The topic of conversation. あの indicates both parties know what they are talking about.
ー＞ I did it
ー＞ Something that I did. ん＝の which is a nominaliser like こと. Generally used for things closer to speaker.
ー＞ Negates what comes before it ie: 俺がやったんじゃない= Not something that I did.
ー＞ result of putting (やっ)た＋ん＋じゃない together:
In Japanese: 〜たんじゃない＝〜のではない＝わけではない＝〜というわけではない
In English: ＝"it is not that ~ but rather that," ; only the ~part of the statement is negated
ー＞ Means same as のです, the sentence ending used for explaining something, and also often to show emotional importance of what comes before it. (So for example, you would tell a doctor: 頭が痛いんです because you want to communicate that it matters.)
ー＞ Equivalent to "but" (like が) and in spoken Japanese the following phrase is often left unsaid because it is obvious from context. It is performing a similar function to the "but, no matter..." in the English translation. (Or to take another example; 「先生、頭が痛いんですが・・」＝ "Doctor, my head really hurts [, please can you give me something for it?]")
ー＞ Means same as ね、〜 "know what I mean?". な is a harsher more masculine version. It is often used to emphasise the importance of what comes before it and to seek empathy from the listener.
If you put all these together you end up with something close to the translation.
I expect you already have references for all the basic components but possibly not 〜たんじゃない because it colloquial? Since writing this I noticed it is covered in the detail of item 3 in 新完全マスターN３、文法, p38.
Understanding this kind of colloquialism is tested at JLPT N1 (聴解). If you want to wok on this you could try one the text books for that exam.