Not sure about right or not, but I use my index finger and middle finger opposed against my thumb. There are 4 corners; my thumb moves between the inner corners, and my index/middle fingers move between the two far corners (the corners on the spine side). The roll of the razor should end when the razor is flat on the strop, in both directions. So my thumb is the guide that indexes the blade flat onto the strop, and no further!
An exaggerated version of the flip is similar to the way some people twist a car key to start a car. Try using a car key to start a car without using your wrist. You see how the thumb kind of "pushes" one side of the key, clockwise, to start the engine? You see how the fingers kind of push in a rolling opposition? Stropping has a similar feel, but the "key" is much smaller.
Put another way the thumb "rocks" the razor back and forth, cradled by the index and middle finger. The contact point of the tip of the index and middle finger on the razor changes slightly for control through the range of motion. Full control of both the flip and the pressure is useful.