Failing to win the German Bundesliga last season I think means that Vincent Kompany will be considered as a good choice if he he can help the club win the league title this season. However, if he manages to also win the UEFA Champions League title which I think will be almost impossible for him, then that will be the best way to shut his critics up and announce himself to the global stage. Just like you said, I also think Vincent Kompany's first major target this season will be to win the league title and then fight for any other available trophy
They have to be realistic in giving Vincent Kompany a target, because he will also need time to adapt with Bayern Munich and it will not be easy to compete in the Bundesliga now, because the Bundesliga is getting more competitive now after Leverkusen showed an extraordinary performance last season. Usually every season the opponent or competitor of Bayern Munich is only Borussia Dortmund and even then Borussia Dortmund has never been able to break Bayern Munich's dominance. This season it is much bigger, because another threat they will get from Leverkusen who even managed to break their record of consecutive champions last season. Now their target is at least to be able to return the trophy to the Bayern Munich public.
Kompany had a much better performance than we could ever expect to see in Bayern Munich from this coach. He was not successful at all recently and he failed before he joined Bayern Munich and when they chose this coach we were not expecting to see this good performance from him because he was not their first and even their second option for this season.
Now considering the performance he had recently maybe now the fans of Bayern Munich can again think about bigger achievements like the Champions League title.