To be fair, I doubt Mourinho would have played Rashford that much if he hadn't already been discovered by LvG and regarded highly by the club as a key youth prospect. It was pretty much a mandatory thing to develop Rashford for any incoming manager.
And while Rashford scored a fair few under Jose, his movement, control and finishing have never been as good as they are now, and that is due to Ole actually coaching him on these aspects rather than claiming "he lacks maturity, his natural ability isn't as high as Sterling's" etc.
A bit of confidence also helps; if Rashford tried out some of the tricks he does now under Jose and got dispossessed leading to an opposition goal or something, he would have to bear Jose's caustic comments post match. Under Ole, he would probably be encouraged to try risky things even with a CB like Jones at the back.