Good scopes aren't supposed to change POI as magnification changes, but what does good mean? Some move.
I sight in for highest magnification, but leave my variables on the lowest magnification for hunting. If something walks by close, I have more field of view right away; its one less thing that would announce my presence. If it walks by far away, I will probably have more time to crank it up, and can get away with a little movment.
Most lower power scopes have the parallax set at a certain distance at the factory. Get far away from that setting and if your head moves it gives the appearance that the crosshairs are moving around in the scope. Its more pronounced in higher magnifications.
An adjustable parallax, set correctly, makes those moving crosshairs sit still. The advantage is gained if you are shooting at something really small, really far away.
For hunting larger stuff in a finite field, I set my parallax at 2/3 the length of the field and leave it there. That way, if its in the close 1/3 of the field, should be an easy shot anyway. For the middle 1/3 and farthest 1/3 of the field, the parallax will be pretty close.