The first time I used prednisone last year I felt the side-effects up till a few weeks after I had tapered all the way down to zero.
Also, once I had tapered below 20mg things got a bit shaky (literally, I got shaky hands - but also had minor flare-ups) so I'm tapering at a slower rate below 20mg this time. I'm on a second course of prednisone at the moment and have tapering down to 15mg.
A few people suffer no side-effects, so hopefully your son's one of them. More importantly it's great that he seems to be in remission or headed in the right direction.