Do civilians panic?

I received my first civilian mission. I got creamed my best guy was turned into a zombie and most everyone died. (and autosave was not enabled)

When I go to replay the mission I wonder do civilians panic?

There were four off to the far left that I spent about 4-5 turns saving while 10's where dying. If civilians don't panic I am thinking the better strategy is kill all enemies then save the pathetic humans