Passport question (Istanbul)

Hello All.

My son entered Istanbul with an American passport and a Visa. But rather than us obtaining a resident permit, we made him a citizen since I am Turkish. He will leave the country next month and wondered if he can leave with his American passport and his "NUFUS" ID even though it will show that he overstayed his Visa. Or is he going to need a Turkish passport to leave with?

Thank you in advance.