Battles interfere with movement. So naturally, if an enemy enters the province of your army, your army stops IF a battle ensues.
However, stacks of units can have different stances, so it may happen that two enemy stacks are in the same province "peacefully" as both are in defensive stance. I have yet to see that in practice though. So far, either the AI or me was on the offensive.
So, you can adjust this "during the turn" behavior of your armies by setting their stance. (there is a total of 4)