Agree with Norman.
This is not considered normal movement and represent an "impetus" bonus to the victorious attackers.
The Eagle system gives several disadvantages to cavalry starting an activation phase adjacent to an enemy, even more with all the added cavalry rules. It is counterbalanced by several rules, which allow cavalry to reposition or countercharge.
So not allowing some reaction to cavalry after advance after combat creates also a special pattern of positioning. Cavalry must either stay two hex away from the frontline or be part of the frontline for reaction charge.