The characters do attack on their own. For example, if you're riding somewhere and pass close to and aggro an enemy, the companion will dismount and fight that enemy on their own even if you keep riding. Since they are always behind you, you might not notice the companion is in a fight unless you have a minimap that shows the companion in combat.
I don't know if this is intended, but I don't mind it.
This happened twice time for me and wife in IC. Light attack without touch the attack button. But it was rare and because pvp is laggy during event i didnt think about it too much...