'Responsible for' and 'most influence on' are two different things. The Maester may have been formally responsible for Joffrey's education, but the relationship between mother and son in this case was far stronger. I can't find anything in the GoT book, but from the TV show witness the moment when Cersei essentially tells him to ignore everything but his own desires (from s1 ep3):
Someday, you'll sit on the throne and the truth will be what you make it.
And a minute later:
You are my darling boy and the world will be exactly as you want it to be.
If that's not putting him on the road to be an arrogant little bastard, nothing is. And of course, as king-in-waiting and member of the richest family in Westeros, he's spoiled beyond belief. The saddest part is that in this very scene he's showing regret and maybe a little fear and humility about the whole incident with the Stark girls, but Cersei beats that out of him and makes him believe it was all their fault instead. Mothering perfection. And the cherry on the cake:
Everyone who isn't us is an enemy.
So to answer your question; yes, his mother was his 'official' tutor. And the Seven help anyone who tried to argue that with her.