Plot hole: There is no reason at all why, being targeted by a few arrows by unseen enemies - a fire suppressed already by the salvo of their own archers - the Rourans would turn around their heavy siege equipment, away from the bulk of the enemy forces, and fire it, hurling a single heavy stone to the middle of nowhere when they have the whole rest of the army who could storm the rock the supposed enemy commandos hide behind, or the archers who could keep shooting - again, they proved to be completely successful. It also makes no sense that the all-powerful witch who made the warriors flee managed to do any of this, 'sneaking' by horse in the middle of the steppe.
Suggested correction: Mulan used the helmets of the fallen warriors to make it appear that a large force has flanked Rourans. Rourans didn't expect this new "force" and knew nothing about it. They didn't know its size. And while their original target seemed harmless, this new "force" was killing Rourans. Fear and death were the reasons. What you see in this scene is an enactment of one of Sun Tzu's famous quotes: "All warfare is based on deception. [...] Attack him where he is unprepared, appear where you are not expected."
What we see in the scene is laughable, and not because of the idea, which surely is based on the profound strategic motto you mentioned and we find in many folkloric tales in other cultures as well; what we actually see in the movie, is that she grabbed a couple helmets lining them up on a rock, and she shot a few arrows. Then she stops shooting, and we see helmets knocked down in their full view. The movie truly surpassed itself in showing it in the most phony way; had they shown her shooting from behind the rock responding to their fire, or the helmets not falling, or them just shooting at mist, terrified, it would have maybe worked. It's an enormous overreaction. That and, under no circumstance trebuchets are used that way anyway. And she did all this setup unseen, again.
In response to death, nothing is an enormous overreaction. Something or someone was killing them. They wanted to kill it, and they didn't have time for Facebook's famous brand of pseudo-myth-busting. What if they knew it was one girl shooting at them? They'd still have done the same. Being killed is a very personal matter.