It goes like this, first round is Surprise, because you initiate combat. So you do your actions, then each of them does their own action.
Then another turn gets rolled. It just so happens you have the lowest sequence, so you get placed last on the turn. So they do another turn, which is the double-turn you see, and then you finally can do something.
So, pro tip, if your perception is lower than your enemies', don't initiate combat yourself. Let them do it, unless you can handle their double-turn.