The main thing, is that Primaris Marines are about twelve minutes old at this point. They are still marines, so they can probably be corrupted in the same way as Mk9 and older marines, but that still is a very situational process.
I don't doubt we'll see Chaos Primaris marines at some point, but I think it's a bit early for them to be doing a foot-heel turn.
I'd also wager that the Badab War wasn't a war between chaos and imperials, it was more of a misunderstanding in force.