You say it's a tremolo issue so...Well is the string cut long enough? Is the hex-nut that holds the string in tight enough?
My Equipment:
Ibanez XPT700
Ibanez A200E
Peavey Vypyr 60 w/Sanpera II
Morpheus Droptune

The little black plastic thing in the saddle could have cracked or worn away, which means a replacement will be needed (dont worry they're quite cheap). Take the black plastic bit out a try and clean out the inside of where it usually sits. This might help.