Because the green system is pressurised, it IS in charge as the automatic selector valve allows the green system pressure to "get to" the brakes.
If the pressure drops too much, then the yellow system pressure is able to "get to" the brakes.
That's correct.
When you step on the brakes, you're actually utilizing a completely closed system, similar to a hydraulic clutch in a car.... at the other end of the closed loop the equivalent of a "slave cylinder" makes all the mojo happen with the green or yellow systems.