It should only be normal to a minimal extent, coming from a guy who drop D-tunes his Jag-Stang live as one of his main guitars at just about every gig for years now. It should not be enough to make a noticeable difference. If the strings are drifting in and out of tune alot, it sounds like one of three things, the tremolo needs the springs tensioned more, the strings are really old and need replaced, or the strings are not properly stretched out.
Solution to #1 is to get a hex key, put it in the 2 holes on that "cigar tube" looking thing at the back (inertia rod?) and turn them clockwise a bit. I typically set them up till the bar is angled about 45 degrees because this causes the guitar to stay in tune better if I'm using the tremolo bar. If you are not using the tremolo bar and prefer more tuning stability, there's always locking down the tailpiece as an option.
On the third issue, you want to stretch the strings out. A common misconception is that the strings need to be fully "Stretched" out to stay in tune, but this is incorrect, you need to have your strings stretched out to the point of equalibrium. If they are stretched out too much, they will either drift sharp over time or will go extremely sharp as soon as you use the bar.
- If using the tremolo, stretch the strings out, then do some dive bombs, this will allow them to compress back to that equal point, after that, the tuning shoud stay pretty consistant, even if dropping the guitar down to D. I find my Jag-Stang only drifts about a fraction of a cent enough to bug the tuner if I do Drop-D. or drop down to CGDGBE, in a live situation that's more than allowable
- Stretch them out, let them sit for 24 hours, then retune,
I also think the string exert a little more tension when stretched to their middle "happy point", ive noticed my tuning really drifts with a fresh set of strings and no stretching being done.
