This was my first time stringing a floating tremolo and I have a question.

How tight should you lock the string down? I figured pretty tight since it seems like it'd just rip right out with all the tension, but I read one place that you should tighten just over "finger tight" and that didn't make sense.

Okay, so I lock my strings a bit tight, not too tight but pretty snug.

Tune up my A string and POP, it pops right out of the saddle.

So I unwind and put it back, and super tighten it. Then I super tighten every string so this doesn't happen. again.

Could I hurt my bridge/saddles if I over tighten? What's the best way to go about this? I can't really find anything on the internet. I have a ZR trem btw.
Tighten it as far as you can really without wearing away the allen key slots, as long as you're using a good quality allen key it shouldnt slip and wear away the slots
The blocks that tighten the string will easily get broken if you put them too tight. They should be pretty tight, but don't get too serious with that stuff. Also, it's quite easy to ruin the allen slots in the screws.

Guitars: Ibanez SV5470F, Ibanez Xpt700, Fender MIM Standard Stratocaster ('04-'05), Jackson Ps-2
Ashton AG200,
Amps: ENGL E530, Bugera 6262-212,
FX: TC Electronics G-major 2, Behringer EQ700, Morley Volume / Wah
I've got a ZR trem and you don't need that much pressure on the blocks. Firm but not too tight.... over tighten and you're going to screw something up....

No disrespect intended but you are putting the end of the string far enough into the bridge so the blocks have plenty of string to grip aren't you???