Time is relative in hexes. Always remember that. Here is an example of how turns would work with overlapping battlespaces.
Suposed that there is 3 sides. Side A, B, and C.
A can reach B, but not C.
B can reach A & C.
C can reach B, but not C.
While I do not know the factor that would determine turn order, lets say that A goes before B who goes before C.
As the start of the day A would go first and B would be aware of this. However whether A or B goes first does not matter to C, all they know is that they are not going first. Additionally, the wonky time flow of Erfworld would assure them that they have enough time to implement their actions in the afternoon like normal. So it does not matter if there is one or a thousands sides before me, all I know is they go before me.
Now lets shake up this logic and assume that A & C go before B. Since C can not interact with A, by my definition of battlespace, both of them in a sense would have turns going on at the same side and both start at dawn. But since they do not share a battlespace it does not matter that they have simultaneous turn. And to B it does not matter who is going first. He still gets his turn in the "afternoon" and since his fights with A can not effect those with C and vice versa (he placed his troops on yesterday's turn and that matter is settled) it does not impact him they seem to be going simultaneously to him. And because of the wonkiness of erfworld time, a ruler could probably armchair general both of them via thinkograms.