Take a stroll with me, I think this might be a decent explanation.
The physics of a cork has to deal with the extension of Newton's first law in rotating frames. Newton's first law states, objects in motion tend to stay in motion. If we extend this to a rotating frame, say for example a rotating wheel, it will tend to remain in its axis of rotation, i.e. if you tilt the wheel while it's spinning, you will feel it want to straighten out again. This is how motocross whips work. The rotation of the back wheel helps bring the rider forwards again (as well as body position).
The same phenomenon occurs when you throw yourself corked, but also with the aid of body position, i.e. the position of your center of mass. If we take that out of the logic however, the underlying idea is the same as a motocross whip but in a perpendicular frame. The body rotates about the vertical z-axis while tipping backwards into the y-axis, given the spin is thrown looking into the positive x-axis (just think regular 3D cartesian frame here). The tipped rotation wants to move back towards the "untipped", or upright original frame as the skier keeps spinning. Remember, this is the same as the motocross whip just in a different frame.
For double/triple corks this process occurs multiple times with the aid of holding your body position to cork "again" after coming upright.
Like I said a couple times though, a lot of this is purely dependent on body position and when one "opens" or "closes" their body to change their moment of inertia, but as a whole I'd say the above is significant portion of the "physics" of corking.
Hope that helps.