Extroverts by defintion show their emotions, Introverts dont.
As such, how sure are you about your observation, given that the Introvert dont show his tilt?
Or in other words, what is tilt? For me it is any kind of negative psychological effect that leads me to play a hand worse than I could in a "neutral" state of mind. As such you can be sure Introverts can tilt just as much as Extroverts you just dont notice it that easily, because it looks different, but has the same effects long term.
On the other hand, there are also both Extrovert and Introvert with high lvls of tilt resistance. I doubt anyone is immune.
As for other personality traits: Just watch high-stakes players, youll notice there are Introverts and Extroverts and both can perform on the highest levels.
So no, you dont have to change your whole personality. Just always improve yourself as a whole towards being a better player. Keep in mind that the best players have done exactly that for many many years.
GL!