Write/call your family and ask them how safe it is.
But you're right that it doesnt sound like a good time over there to be associated with Gulen movement to me.
But to change the subject slightly: thats sad news that Turkey is turning repressive. The Gulen movement (all I know about it is what I just read on Wiki) seems to be nonviolent. Neither violently subversive nor terroristic so anyone arrested for connection to it is a political prisoner. No justification for the repression of it in a democracy.
Further- the Gulen movement (imperfect as it may be) sounds like just what the Middle East needs- a political brand of Islam that is allied to the future and not to the past: and that is okay with democracy, capitalism, and interfaith dialogue. A possible alternative to Salafism/Wahabism.