Rules don't really mention it, as Stand Still isn't any sort of general combat manuever, i.e., trip, disarm, overrun, etc. I believe handling it the same as a trip for a mounted combatant would be a fair DM adjudication.
Edit: Although the "as if he had used up his move actions for the round" language could be interpreted to mean his mount can keep moving, but he wouldn't be able to make a move action.