I don't pull it into reflex, no. You can of course, but exactly as you say it causes problems later if you want to go over the bow again at some point.
Let's say the stave is dead straight, and you've done all the tapering and finishing and nocking etc. You get it up to the full brace height and you notice straight away that one area is weak, or will end up weak or whatever. That's the bit you tag with the heat gun - but after just bracing the bow there won't be any set there, so you don't need to induce reflex as well. All you want to do is add strength to that one small area.
As to other point, yeah I tend to heat treat and leave it until the belly feels completely cold, then just carry on tillering. There's really no need to add oil, or wait days for the RH to return etc, you can get it bending again almost straight away. You just have to wait for all the heat to leave, otherwise you risk "heat bending" the area into permanent string follow!