Maybe you're just getting used to the sessions. I tend to get DOMS from Tuesday PT on Wednesday night. This week it was only the right glute, possibly because I only did half the pushups that we were supposed to do so nothing in the pecs.
Maybe, but I have been doing the same session every week for more than 12 months and was still getting tight around the hips a couple of weeks ago. It might be a lot worse in the afternoon because I do tend to sit at my desk without moving for 8 hours at work.