I've played TBS games where a unit's move stat was also used in the battles. When battle had commenced, the space the battle was in was zoomed in and revealed to be composed of many smaller 'spaces', and the units had their amount of move to use per 'turn' of battle. The battle would last either until one side won or either side withdrew. Perhaps something similar is at work here.

As for timing, I think there might be something to the 1 turn in combat = 1 move outside of combat theory. Ansom was 3 move away from Jillian when she sent the thinkagram. Then say we count the Archons' opening attack as 1 combat turn, and Jillian's 'Boom! Headshot!' stunt as the 2nd, that would have Ansom arriving right at the 3rd combat turn and getting to Jillian just in time to yoink Manpower.