This is probably because on a road bike you're often going faster than what you would be on the hybrid. A common trick is to raise your pedal on the side that you're taking the corner, so that you don't accidentally clip your pedal on the bitumen. I mean if you're turning left, make sure that your left pedal is raised. Make sure that your hands are on the hoods (where the brakes join the handlebars) and apply a bit of the pressure to the side opposite where you are turning to balance things out a bit. So for a left turn have your left pedal raised, lean to your left, but apply a bit of pressure to your right hood. This seems to work for me.