yeah, if your bridge is lifting out more then before, your new strings are probably a thicker gauge then your old ones.. so what you want to do is open up the back cavity plate, and see the two screws, screw them in tighter, then retune, see where your bridge is at.. and repeat.. the idea is to get your bridge to be flat over top of the body, floating over it a bit. you don't want the bridge like this: / or like this: \ you want it like this -

so, let's say here's your guitar: __________----____ that's what you want it to look like. ok?

also, you don't want to adjust action using the saddles, those little screws in the back of the bridge (your bridge in particular is called a tremolo, btw) because those adjust intonation, which is a whole different ball-game.

and yes, the tremolo on fenders are meant to dive bomb, and be pulled up too. give it a try, see what sounds you can make!