I can attest to this. I have a Thrustmaster Hotas 4, and was having this problem - I went to the sensitivity panel for it, and then just moved the stick around, and let it go, so it would snap back to center. From that point I could watch the sensitivity cursor literally vibrating along the curve, sometimes beyond the dead zone I had set. Expanding the dead zone beyond that range was an enormous help.
So I guess I’d add to this solution - set your dead zone, but definitely watch how your controller behaves while in the sensitivity panel, as that can inform the size of the dead zone you create!