in a game with rules like this thoughts can be neatly divided into "after seeing the results of turn one, and before deciding what to do on turn two," and that is all that is important.

I don't know as to how that maps to "simultaneous access to the same information", however, in any computationally significant sense. It's simply a characteristic of the definition of turn-based as opposed to real-time 'games' that you do your processing between turns but during real-time.