Yes, student pilots in the beginning of their flight instruction frequently overcontrol. This is typical and normal and most easily seen during final approach where the aircraft rocks from side to side. The tendency to overcontrol will be reduced with experience as motor controls improve so I wouldn't worry about it too much at this early stage.
To correct this tendency, I would:
1. First recognise that I am overcontrolling. A cue for this would be when you start saying things like "S*#t, why the f*$# can't I fly this thing!" to yourself.
2. Relax the grip, take a deep breath, trim the plane and use small controlled movements.
I would say there can be a tendency to concentrate so much on your objective that you detach what you're thinking to what your hand is doing and if you can consciously think about your hand movements it may help.