On the android version they move back a little bit and indeed your soldiers announce it. I don't think they hunker down (the only time I saw an alien hunker down was when being suppressed), but maybe they go on overwatch. It's awfully annoying when they retreat and engage 1-2 more alien pods too.
Your soldiers can also panic. It never happened to the soldiers I started with (they gained willpower faster than the aliens could scare them with), but I once brought a bunch of rookies to a mission with mutons and yup, panic ensued (mutons also have an ability that causes panic in low willed soldiers).
The best was my heavy squaddie who unloaded his whole machine gun point blank into a muton berserker after panicking from being approached, managing to kill it before it struck. Close combat isn't very scary when you only get 2 action points. As long as you are just far enough, the enemy just plants itself next to you and you can shoot them with 100% accuracy next turn.