That is not what the diagram is showing you. That is the wiring between the indoor units and the wired controllers. It is not the power and control wiring between the indoor units and the outdoor unit. I am sure that if you remove the covers on the outdoor unit you will find a place to land three wires plus ground from each wall unit.
You probably don't need a wired controller. The thermostats are in the wall units, and not in the wireless remote. There is a thermostat in the wall controller that you can use instead of the one in the indoor unit. You can walk your infrared remote around to each indoor unit and set its temperature set point and other control functions. However, each indoor unit needs a home run to the outdoor unit with three wires plus ground. I use
#14-4C THHN-PVC Tray Cable for the runs to the outdoor unit. My experience is mostly Mitsubishi and I have never installed a Gree, but from the manual the principles are the same.