He apologizes because it's Japan, but also because it's a great opener for reconciliation. He was in a good place for making up, but other dude wasn't even close. Apologizing for his parts brings the topic to what needs to be talked about without other dude having any reason to prep for war. Instead they managed to talk it over and get through to a good closure. Perhaps dude will apologize later, perhaps he won't in words - as long as a good working environment is reached, that's what the Producer really wants. (And it's good training in managing prissy actors later, which has nothing to do with age or past deeds, just with personality and experiences.)
Tbh, the easiest way out of a family fight is also to apologize first, whether you're the "more guilty" party or not. (As long as you're stuck in the "assigning blame" phase you won't be able to get to where you should go to reach peace.)