I've had a similar experience when it comes to crits. This is just my first season of racing so I don't have a lot of data to go on. However, I have noticed that the crits that I have done well in were those were I noodled around for 2 hours prior!! the first hour was just riding around at a relaxed pace, much like what you described. The second hour was a combination of tempo plus some hard efforts. The second hour wasn't that structure 0 meaning that I wasn't paying attention to my HR, but I'm just guessing what the zones were based on how I felt (RPE). During that time I was actually doing a pre-race clinic so the hard efforts came from the sprints that we practiced. The "tempo" work was when we practiced rotating pacelines.

For RR's and TT's I've just done the normal pre-race warm up that I got from my coach and that has worked out ok. Crits go fast from the gun and if I don't do a really, really long warm-up then I generally don't feel good until halfway through the actual race. I don't have an explanation for this. I'm guessing that it has something to do with my lungs opening up. They don't seem to like hard efforts without a lot of easy stuff beforehand. I don't know if everyone is that way or not.

For RR's they generally start off with a promenade which is enough for my lungs to feel open even if I did minimal warmup before that.