Yeah that is normal. As I said with a floating trem, the tension of each individual string is reliant on all the other strings, as it's their combined pull against the springs that keeps the trem level.
So, if you lose some tension in, say, the E string, the tension is increased on the remaining strings since the pull of the springs remains constant, while the
string tension has weakened. When you're tuning, youre narrowing down the relative tensions of the strings until they are all at the tension you want them at, so it takes a few tries.
You shouldnt need to be using the
tuning pegs regularly though. How much does it go out by and do you use the micro tuners to correct it?