What I found helped was being slow - if for example you're drifting left, do NOT try to add enough right cyclic to immediately stop the drift because you'll just drift right. Instead, add a tiny bit of right cyclic and see what happens. Probably you'll stop drifting after a second or two. Then you can add a touch more to drift right to get back to your spot, then a tad left to stop the drift. Overcontrolling is extremely common.
yes, a standard demonstration of hovering is to show a change in attitude that causes a drift (to the left for example) and then reselect the hover attitude which will gradually bring you to a stop but in a different place.
Reacting to the movement over the ground is much less effective than reacting to a change in the hover attitude - hence people who can hover well make small, gentle cyclic movements in reaction to seeing the aircraft attitude change away from the hover one.