If an American student commits a crime in Turkey, we wouldn't call this student a "Turkish student." Some universities in Turkey may not be wholly funded by the Turkish government, nor culturally and financially indebted to a Turkish family.
I think the question would more be of an American who moves to Turkey, then ten years later goes to Russia and commits the crime there. Is this person a Turk or an American? They don't live in the USA; it doesn't make sense to call them an American.