I don’t have experience with this controller, but I would have expected the button LEDs to light up when they are set up in’ toggle’ mode in the controller.
On the GP side, in the widget properties for your button widgets (MIDI tab), the ‘Sync’ button will send the MIDI message back to your controller when you select the widget in GP.
What the controller does with that MIDI message (or not do) is completely up to the controller.