We are fairly convinced it puts the car into front wheel drive mode too and cancels out the rear motor.
Not me - seeing that Mitsubishi tells us it is a permanent 4 WD with the rear motor always powered up, although it may not be contributing much in certain situations. The anti-yaw system, for one, needs permanent power on all wheels.
If there is no arrow showing to or from the rear wheels it does not mean that the motor is shut off. It means that the power flow is neutral at that moment. If the motor were really shut off it would need a clutch to disengage it to prevent dragging.
It can easily be proved too. On a slippery road at speed stabilize the car so that the rear wheels are idling, so no arrow. Then give the steering wheel a flick left-right and you will see the arrows flicker and feel the rear wheels bite. Don't try this unless you know how to control a skid on a heavy automatic 4WD, though.