shin-bangyes def not a power drill. just use a screwdriver and tighten them (if you can) but just dont strip the heads of the screws. also what bindings are they?
It isn't the heads you should be worried about, if you tighten the screw too much you will strip the hole and have absolutely zero hold meaning you will need helicoils or another sort of threaded insert (which is what veng_m was talking about).
It is hard to say if they are pulling out since you don't know what it was like before. My guess would be that whoever did the mount didn't realize that they left the gap, either way minimizing the gap would be a good idea if there is any sort of play with your bindings.