Heavier strings pull the bridge up and forwards, lighter strings don't pull as hard and bridge goes down and back
It needs to be adjusted for otherwise your intonation will be shot, strings will sit too high/low, fret buzzing...
You need to remove the big plate in the middle of the back of the guitar, then with a big cross head screwdriver tighten the screws that attach the spring claw to the body if you have heavier strings, or slacken them if you have lighter strings.
How much? It depends on lots of other factors, but the simplest target it to get the Trem back into the position it was in before you changed the gauge.
This is standard trem set-up and applies to any trem equipped guitar.
This document covers an awful lot more related to setup of the JTV-69 Trem - photo on top of page 7 shows the springs, claw and the two screws.
[won't even start about whether the claw should be parallel to the body or tighter on the bass side.. ]