I'm not an expert, but I had "Zoysia" on my Missouri lawn sharing turf space with "Kentucky Blue".
Obvious characteristic was the late greening, early browning with the change of season.
Now with my Bermuda Texas lawn, it seemed to match the same greening/browning cycle.
Zoysia won't crowd out your Bermuda (more like the other way around), but since the Bermuda doesn't do well in shade, they can live harmoniously.
I'm using fescue on the shady areas right now. It's not in a highly visible area of the house, so I don't mind the solid green patch that lingers long after the Bermuda has turned brown...