The problem is that they're still a little wet underneath, so it's possible the screen protector can slide around or get peeled. It's not really necessary to actually turn the phone off, but you should let it sit a little to dry first.
I've gone through 4 different protectors trying to find one that works with the bumper since I got my phone about 3-4 weeks ago. When I apply wet protectors, I try to do it before going to bed so that it can sit for 8 hours. If I do it during the day, though, I try to give it close to an hour to dry a bit first (clean up after applying, take a shower, etc.). Then I'm just really careful with how I handle it and where I put it for the rest of the day. Set it down carefully and try not to have it in your pocket much so that dust doesn't get underneath the edges. It's probably a good idea to try not to use it heavily or do anything that will make it get warm/hot so that the screen protector sets properly. Normal use will be fine, though (occasionally surfing, some texts, and a few short phone calls). If you're using a case, you should try to wait 2 days before putting it on.
P.S. If you have the time, please consider adding a short review to
my screen protector thread (especially if you're using a bumper).