I am right-handed, so when my cheek touches the comb

it results in pressure from the left applied behind the rifle's center of mass. So my shots displace to the left.

With a decent scope, if your objective is properly focused on the target - and the eyepiece is properly focused on the reticule (I won't go into detail here...) , then eye movement will not result in a change in the POI - that is why the focus adjustment is also called the parallax adjustment. There are probably more topics devoted to sighting in your scope than I can shake a stick at, so to be brief - if you set your rifle down on some pillows or bags and set it up like I described above and sight through the scope without touching or disturbing the rifle, you should be able to move your eye up/down & side-to-side without the crosshairs moving relative to the target.

Tom