It was a chase scene. So rearranging the turns so Jillian's crew got two turns to Stanley's one allowed them to get in front and lay in ambush.
1. Stanley moves
2. Jillian Moves
3. Change Sides.
4. End Turn
5. Jillian goes again
6. Stanley goes.
So it definitely provides some advantage in limited situations. Passing a special unit with a critical ability that will be doubly effective if used twice. Maybe make some golems, get passed over, make more golems. Chase scenes also allow a side to effectively get two move actions to another side's one.
Normally splitting a side is disadvantageous, but sometimes the side is already split. If that's the case then special units then can be passed around for a temporary doubled effect.