First, I think the civ-limit mechanism is definately in need of refinement / rethinking.
BUT (You know it was coming) - humans, especially panicced, untrained civilians, are STUPID animals. They DO run into danger. They do stuff that is illogical. When the nice big soldiers appear, unless the civilian has seen and knows it's aliens attacking, may very well think it's a military attack. If they do recognize the soldiers as the "good guys" - and the good guys with the big protective guns are moving in the direction opposite of the "safe place" they've just been instructed to go to, they may not go there. After all, who is there to protect them? What makes THAT place safe?
Humans are stupid, illogical, panicy, ANIMALS. I'd like to give us more credit than that, but honestly, I don't think history would support it.