If it is just soreness, not pain, then I would say that your assessment is correct. The problem a lot of pitchers run into is that they throw a lot and work on the muscles to accelerate the ball, but they do not work on the muscles that decelerate the arm. Your son should be doing band work and light dumbell work to strengthen the back of the shoulder. Really he should be doing them to strengthen the whole shoulder, just don't neglect the back.
My understanding is that one of the biggest dangers with pitching off the mound too much is that it is much more of a strain on the decelerator muscles because you are going downhill. This helps with forward momentum, but makes it harder to decelerate the arm.
I don't think it's unusual to have some soreness for a couple of days. My son is usually sore the next day if he goes over 80-85 pitches. I usually don't have him throw the day after he pitches. The day after that, even if he is sore, I encourage him to get out and throw to start working that soreness out. I would also have him ice his shoulder after pitching outings. There are opinions on both sides of this practice as to whether it actually helps or not, but once my son got to the velocities you are talking about with your son, he has been doing it as a preventive measure.
I'll echo what CADad said. I'm not a doctor, but I think as long as what he is feeling is muscle soreness and not pain, he should be OK. And I would really have him do some exercises for the back of the shoulder in particular.