Here is a photograph of the Seiko Magic Lever. The rotor has been removed.
1. The Intermediate Wheel and Eccentric Pinion.
2a and 2b. The Magic Lever.
3. The Intermediate Wheel and Pinion.
4. The Ratchet Wheel.
How the system works.
When the Intermediate Wheel and Eccentric Pinion (1) rotates clockwise, it will 'pull' the lever (2a) and that lever will pull the Intermediate Wheel and Pinion (3). When the Intermediate Wheel and Eccentric Pinion (1) rotates anti-clockwise, the lever (2b) will 'push' the Intermediate Wheel and Pinion (3). So regardless the direction of rotor rotation, the Ratchet Wheel (4) will turn and wind the mainspring.
You can see the motion in the video below. In this video, you can see that regardless of the direction of the rotation of the magic lever, the barrel rotates in a single direction. I read that it takes about 160 to 170 turn of the rotor to wind the mainspring arbor one rotation.