This is not normal. Because here is the letter from Conway telling Trump he didn't want the job being offered.
I mean, seriously, folks, among many bizarre things about this is the sheer stupidity of it, does Trump not think there are records of such things???!! Yes, yes, I know the various explanations of how he operates, and that Trump never thinks he'll be caught, but still... This is dealing with a very high-level lawyer. Even low-level lawyers keep documents. Has he not learned that YET? Hey, he should know that some lawyers even record their conversations with you!
The only thing that makes a hint of sense to me is that Trump is so nuts that he can't take rejection and in his mind George Conway didn't turn him down, and he (Trump) really was the one doing the rejecting.