There is nothing wrong with your tuners, your strings are just going #### and you're using the whammy bar too much, probably causing your intonation to slip too, or rather, become more apparent at it's poor setup.
The whammy bars make you go out of tune, it's a matter of fact.
It is impossible for tuners to slip though, so it's not the tuners fault. Is it possible your nut is squeezing the strings and making their tunings flux?
The way tuners are geared, no matter how cheap or expensive, they do not slip, it's impossible. Take a pliers and grab the string post, and try to turn it the "wrong" direction, it'll never work. People waste money all the time on new tuners and it's the dumbest thing you can buy.
I mean, expensive tuners have a better gear/turn ration so that you can get more accurate, but once you're done spinning it, it stays put just fine.
And if the Jagstang has tuners anything like the mustangs, they're really accurate.