Hi and welcome to the forum!
This is not a feature of this guitar neck, or indeed of any guitar. If the wood was unstable I would expect large changes in neck relief with seasonal changes in humidity, and that results in unwanted changes to the string height. (The appropriate remedy is to adjust the truss rod to bring the neck relief back to where ti should be, thus restoring the correct string height). That can occasionally happen with a neck from any manufacturer because there are always a small percentage of pieces of wood that react strongly to changes in humidity, and yes thinner necks may be more prone to it, but it is not a common complaint of any Music Man guitars. Also, I'm not sure this is your issue because it's normally month-to-month or week-to-week issue, and not a minute-to-minute issue.
Diagnosing this problem is always difficult over the internet and a good guitar tech or luthier needs to see the guitar in person to diagnose to correctly. Having said that, I will suggest the following...
1) If your bridge is set to float (allowing the tremolo to pull up as well as push down) tuning can be sensitive to the position of the guitar and to pressure on the bridge from your hand. This particularly noticeable if you use just two springs in the rear cavity.
2) Make sure the neck is correctly seated in the neck pocket and the neck screws are appropriately tightened (but not too tight, you could crack the neck plate).
3) Adding lubrication to the string slots in the nut, and to the top of the saddles, should improve tuning stability. I recommend something like lithium grease, vaseline, chapstick, pencil lead (graphite), just a small amount. And of course tuning stability is always going to be terrible if your strings are old and worn.