Mbappe obviously has a massive ego. He grew bigger than Paris Saint-Germain - and he knew it, so he effectively did whatever he wanted at the Parc des Princes.
There are also concerns over exactly where he fits into Madrid's starting line-up. His arrival wasn't exactly essential. In Vinicius, Madrid already have one world-class left winger. Now they have two, evoking memories of Perez's bizarre decision to bring in Beckham when he already had Figo for the right flank.
However, it is in both Mbappe's best interests to make this work, so we're unlikely to see the same sort of petulance we witnessed in Paris. He can't really afford to rock the boat at Real. After all, he needs Madrid to win the Champions League - not the other way around.
It's, therefore, likely that he'll continue with the charm offensive that started years ago, talking constantly about the realisation of a childhood dream, and playing wherever the coach wants.
Besides, the word is that Vinicius and Bellingham are already looking forward to lining up alongside Mbappe - although whether Rodrygo is quite so excited is another matter altogether, given the obvious threat to his starting spot. Remember, another budding Brazilian superstar, Endrick, is on his way from Palmeiras too, meaning Madrid will be overflowing with attacking talent next term.
Still, while there will obviously be tricky tactical and interpersonal problems to resolve, who better than Carlo Ancelotti to figure it all out? He's Perez's present-day equivalent of Del Bosque - only this time around he has no intention of disrupting the delicate dressing-room harmony by ditching such a calming presence.
Perez also now fully appreciates the importance of solid foundations, which is why he's spent the past few seasons signing young midfielders such as Aurelien Tchouameni and Eduardo Camavinga. The word is that Lille's teenage defender Leny Yoro could also arrive before the start of next season.
Perez, then, is perfectly placed to usher in a new era of success at the Santiago Bernabeu, built around the combined brilliance of Mbappe, Bellingham and Vinicius - which really isn't good news for Barcelona and the rest of Real's rivals, but represents a thrilling thought for Madrid supporters everywhere.