Gulen was a supporter of Erdogan from the get go... when Erdogan was clearly an islamist.
Their break, if there is one and it’s not just for show, was over ethical purity- or Erdogan’s family’s lack of it.
So I am not so sure Gulen is really a moderate. He seemed fine with Erdogan’s turn away from secularism, only getting weary of him when Erdogan’s son got caught in some financial fraud scheme. Remember that the word’s press considers Hamas to be moderate because they are the political wing rather than the military wing of the Muslim Brotherhood.