The "parabolic stroke" is merely hanging the mirror over the tool more than with the short polishing stroke. It's kind of hard to tell you where to stop as different laps do different things. The thing here is to not do too many strokes as you can easily overshoot the desired figure which isn't a result of any particular stroke size but rather a particular stop along the way of a hyperbolic figure.
You do want to keep rotating the mirror on top of the tool as this is what makes the surface a figure of revolution rather than something else.
If you read what somebody did to get to the desired result, you really can't do exactly that and get to where you need to go due to the variability of so many things, including the temp of the room that you are doing the work in.
The best thing is to sneak up on the parabola and don't let the thing get away from you into hyperbola land. If you do, the best advice usually is to get the sphere back and start again.