I just kicked some stalker butt - how'd I do it?

I found a couple of reports where people claimed stalkers on rooftops are just weirdly glitched. I think the game spawns them on the roof but then doesn't really know how to get them "stalking" properly. It wouldn't surprise me if encountering them on the roof occasionally triggered other glitches.

Apparently also turning around at the last moment causes Ezio to push them down instead of the stalker grabbing you (according to part of that thread which I apparently skimmed and did not fully process...), so maybe it's a combination of the two?