Yeah, the advice in the first few posts is exactly what you should do. Everything needs to be set up, stretched, and then tuned to pitch, lock the strings tight at the nut, then use the fine tuners to get it perfect. It should be stable at that point. Just remember when tuning with the headstock tuners before you lock to give yourself some travel on the fine tuners, in general the guitar will go sharp when you lock the nut down tight, and you need enough travel on the fine tuners to compensate.