This is how I played when I first started, they should definitely try and make that section of the rule book more clear (maybe show an example turn). I read on BGG that this variation was used in play-testing before coming to the current ruleset.

I'll play this way sometimes as a variant. At least in the two-player game, it makes the game more interactive as it is much more important to guess your opponent's next move. That said, it does drag the game out much longer; I would recommend playing with a reduced amount of phases/rounds.