Bey means Mr? The exact same word in Urdu is used to talk to someone disrespectfully. This is really strange because there are a lot of similar words in these languages.
So it seems they put titles after the name. Does that mean Turks normally say their family name first and their given name last?
For example, would Recep Tayyip Erdogan be Erdogan Recep Tayyip?
no we never do that.
we just use our family names less often. It is very unusual to use only family name actually, we either use both or only the first name when we introduce ourselves or when someone is talking to us/introducing us. The only exception is politicians, but even then it is often still normal to say "[First Name] Hanım/Bey" instead of "Sayın [Family name]".