here are three inter-twined parts to the process of creating gyro- stabilizing torque. Note that each of these things is simultaneously occurring at the same instant in time, but it is helpful to consider each of them separately. Once the flywheel is spinning, the following process leads to the development of a stabilizing torque that opposes rolling motion:
Waves cause the vessel to roll
Rolling motion combines with the spinning flywheel to create precession motion
Precession motion combines with the spinning flywheel to create stabilizing torque
The physics that causes these inter-twined actions is called gyro-dynamics. If the flywheel spins in the opposite direction, the induced precession motion will be in the opposite direction, but the stabilizing torque will be identical.