Here's the situation:
I have two army figures on my Academy. I'm attacked by two army figures from another player in his Movement phase. He has the Combustion tech.
He wanted to use the Combustion tech to destroy the Academy before the battle took place. I argued that he wasn't able to do that, and only after we finished resolving the battle would he be able to use Combustion to destroy the building (assuming he won the battle and still had figures left on the square to kill it off).
My argument is that his army figure's movement does not count as "complete" until the battle's resolved, and the Combustion ability only works when the unit finishes it's movement on a building.
You have it correct. As soon as a unit moves in to a space with an enemy there is a combat, when the combat is over that unit's movement is over and if he won, he could destroy the building. If it was a walled city it would destroy the walls (because it says it does).