Yeah, that sounds as a bad set up. FRs are a pain at the beginning, but if adjusted properly, they should keep tuning no matter how agressively you use it (in a reasonable way, obviously).
When was the last time you changed strings? As daretofail puts it, when you change them you have to stretch them a lot all over the fingerboard till they settle down. I don't know if you did it, but I find it very important to make sure the stability of the tuning later, so I take a long time doing it everytime I change mine. After that, I just play chords and stuff to make all strings work together, and sometimes put the whammy bar down and up to help the strings adjust, with no locking nut caps and repeat again until the tuning is totally stable. It takes me a few hours but after all this process, I put the locking caps again and it usually keeps tuning until the next time I change strings with little or no fine tuning correction, even if I get crazy and use the whammy bar sometimes.
I hope it helped you, otherwise, just keep asking
