There are plenty of menus here that show Turkish's late night services.

A supper will be served after takeoff, and then breakfast prior to arrival.

Despite on demand dining is listed in menu, TK F/As just assume that everyone will dine at the same time, unless you specifically request it.
Honestly to get used to US time, I will personally stay up a bit for the supper service, and then sleep till breakfast which will typically be served 2 hours to 2 and half hours prior to arrival. Regardless, if you want dine later, you must inform the F/As when they take the meal order prior to departure. Food cannot be reheated again and the leftover starters/soup/dessert are all crew meals. If you don't ask them to save you food, you will get nothing. Their mid-flight snack menu is pretty weak and you will be lucky if they have some cheese sandwiches available.

Carfield