Mbappe's time at PSG was uncontrolled and arrogant due to a lot of pressure. Many media only report on Mbappe from the bad side even though we all know he is like that because of a lot of pressure from the club owner. But now that he is free from this pressure after joining Real Madrid, he admits that he is very happy to finally be able to join Real Madrid and be free from the shackles of PSG. He will not disappoint Perez and Real Madrid, he will do his best for Real Madrid because Real Madrid is his childhood dream team. So, as you say, he is worried that he will cause problems at Real Madrid, this seems unlikely to happen, especially because he is old enough to control his emotions.
It cannot be denied that another reason he moved to Real Madrid was that he wanted to win lots of trophies and the pinnacle of his individual achievement was the Ballon D'or, and that was very natural because he was a talented young man. My prediction is that Mbappe will quickly adapt to Real Madrid's game because he fits very well into coach Ancelotti's scheme with players who have high speed.
The boy was literally doing what he likes and I don’t think any club will treat him better than psg, and if it’s about pressure I don’t see anything bad from the pressure they are given him, the boy is good so they want him to do his best because that is what is been paid to do. And his stay with psg will be the best because even his pay was very much okay, he had only one duty to perform which was for him to do better, and even if his happy he still needs to do better, and everyone knows that one of Mbappé dream is to join Real Madrid and since the dream is now reality. The only thing I have to say is that Mbappé needs to work with his newly team mates to archive more trophies because one key thing is team work if the players have good team work then they have less problems to deal with, and since is not his first time of playing that shouldn’t be a problem.
I love the fact that Mbappé has goals he wants to archive even has young as he is, and he knows that only in Real Madrid he will be able to win those trophies and if it Ballon D'or then it is something he can win he just needs to push him sell hard since he is now in Madrid and as for psg can not really say much since Mbappé have even left the club. Mbappé and Ancelotti we work together since they already have a target they want to meet Ancelotti needs more trophy in collection too.