Hello
Correct me if I'm wrong, but first you setup ALL of your miniatures in your deployment area (this area and the way you deploy your forces may vary according to the scenario, some character have abilities which allows them to be deployed later, but it's a special case). Then, when both forces are on the table, the player who "owns" the Domination chooses which side begins. The chosen side activates one mini, (or two with Vae Soli) then his opponent plays one (or two) mini in the same fashion, etc. As far as I know, you can choose freely which mini you activate.
I hope this will answer your question.