I don't think anyone knows for certain if they promised him the job. He might have seen the writing on the wall with J Smith and put himself in the best position to win the job. Like they said on FRL, Coleman was basically a for sure hire at OkSt because of where he positioned himself, but if he didn't move to OkSt, would he be the #1 candidate? Not sure he would be. Very smart strategic move from Coleman regardless of if they promised him anything.
Also, Coleman has gotta be salty either way. If DT passes on this, he's the third choice and wins by default. Who's to say he won't be on the chopping block in the future. Not sure how I'd feel about that if I were him.