Ha! I'm so glad you are confused about that! Because that's a thing I've asked everyone, everywhere!
Ok, talking about American English... as far as I know (what I learned), sometimes when you have a N followed by an S, you get an "intrusive" T between them (call it what you want). And that happens with N + SH too.
Before I learned that feature, I mispronounced all my N's, so I used to pronounce PRINCE and PRINTS quite differently. Now they would come out pretty much the same. Merriam-Websters points out that phenomenon in its transcriptions: PRINCE is /prin(t)s/ - they put a T in parentheses.
The problem with N + SH is that if you put a T before SH, T+SH is very similar to CH (as in CHERRY). So similar that IPA transcriptions actually use /t/ + the symbol for SH when they want to give a transcription for CH... --> t + ʃ = tʃ
However, it seems T + SH is not exactly the same as CH, at least when speaking at normal speed. In other words, MANSION is actually MANT-SHUN, which sounds very similar to something like MAN-CHUN, but it's not exactly the same.
I can't be 100% sure though, because it's something I've never really understood, but in my opinion T + SH is not exactly the same as CH at normal speed, so MANSION is not really MAN-CHUN, but it's MANT-SHUN, which sounds very close. In fast or careless speech (or in songs), I'm afraid you're gonna get a real CH sound though.
Just my opinion.
By the way, this issue comes up when you look at certain transcriptions in some dictioneries. My Longman and Oxford both say CENTURY is SEN-CHURY, but Merriam-Webster gives SEN(T)-SHURY instead. This is confusing, darn.