>Not my problem is not even a common phrase. "This is not my problem", "well it's not my problem" is common to some extent, but just "not my problem" is virtually only used in nuWeb form
That's not true, although it's definitely a case of informal vs formal (and Heyuri is very informal ), and I suspect it's also somewhat regional

It's very common where I come from to not include the subject at the start of a sentence - you will regularly hear/read phrases like "not my problem" over "it's/that's not my problem", "can't be bothered" over "I can't be bothered", "don't care" over "I don't care", "looks stupid" over "It/that looks stupid", and so on

Just for fun, I did a search on old.sage.moe for "not my problem", and here's some of the earliest examples that show up (keeping in mind there are big gaps missing in the archive):

https://old.sage.moe/r/thread/61098/#61196 (Feb 2005)
https://old.sage.moe/b/thread/6935505/#6935599 (Apr 2006)
https://old.sage.moe/b/thread/7457956/#7458020 (May 2006)
https://old.sage.moe/b/thread/7894158/#7894329 (May 2006)
https://old.sage.moe/b/thread/8917577/#8920072 (Jun 2006)
https://old.sage.moe/b/thread/9083140/#9087046 (Jun 2006)

Also, a quick search showed me that the 17th episode of the Animorphs TV series was titled "Not My Problem", and that aired in 1999: https://en.wikipedia.org/wiki/Animorphs_(TV_series)#Episodes

So regardless of how kiddies might be using it outside of Heyuri in recent years, I think it's safe to say it's a common and old phrase... which I already knew since I've said it my whole life

>Regarding the question of normie/normalfag: while normie is certainly very old and normalfag is far newer, normie made a resurgence as an attempt to purify 'normalfag' 'discussion' for use outside 4chan and entered 4chan parlance through the increased volume of outsiders posting there
Thing is, Heyuri has been trying to stave off the grumpy group of late-2000s to mid-2010s imageboard users who were butthurt over "normie" being used instead of "normalfag" circa 2015 just as much as it is staving off those who were/are commonly using it. That's why it's best to use neither, or just not care about it at all