This is all assuming that you have a Floyd Rose type trem. I have no experience with a Kahler.
Basically it's just a balancing act. If the trem is coming up on you, loosen the strings a little and tighten the springs a little, check tune, and repeat. And obviously, do the opposite if it's too low. You will want to do this gradually, a little bit at a time, that way it doesn't get away from you and go the other way. After doing it enough you will be able to move more at a time. After it's in tune and the trem is level, you can lock down the nut.
Also, in case you don't have the spring set up this way, for some reason it helps with stability if you install the springs so that they are on the middle 3 hooks on the claw and in the middle & outer two holes in the block, forming a kind of triangle with a spine up the middle, so to speak. This is assuming that you're running 3 springs.