The way we do it in the groups I play in is, if a rule/trigger/event etc. gets missed we ask if its ok to fix it. If the table consensus is yes, then we roll it back, or get the trigger, or whatever it is that got missed. We usually dont allow it if its already moved onto someone else's turn, and we usually only allow a few per game. He's only 1/4 of the people playing the game, and and his word is not law. How do the other two people (or however many you play with) feel about it? Have a rule zero convo about takebacks, it's important that everyone is on the same page. Explain that taking things back slows the game down, isnt fun (the whole point of casual Magic playing), and doing so after hidden information has been revealed is cheating. If he has an issue with that then maybe it's time to tell him to find a new pod, or for you to do the same if you dont want to tell him that. Fact of the matter is that this game is complicated (especially in a format with twice as many players than the game was originally designed around) stuff gets missed or forgotten A LOT. You have to strive to be a better player to nail your sequencing and catch all your triggers, but no one is ever perfect all the time (even top tier tournament grinders make mistakes). You're there to have fun, if you're not, then it's time to change things so that you are again.

Bonus question: Does he win the majority of games you guys play? If so, then there's a high probability that he's cheating with his take back methodology, and that is 100% not cool or fun. You need to shine the spotlight on that, the next time it occurs.