I know that Jack later mentioned that Jesse ratted him out to Hank, however I have heard that Jack is a “darker version” of Walter White and the fact that he already had the tape and it wasn’t in the hands of the DEA, as well as the fact Hank and Steve are dead, I would imagine that he shouldn’t have cared that Jesse admitted it.

I feel like he got upset for a reason like his pride was hurt, similar to how he reacted towards Walt in “Felina” when he said that Jack was partners with Jesse. I don’t know, that’s just my assessment.