Looking at the board, it looks like each input has 2 connectors, so both wires for each button would go there.
I found the encoder on Aliexpress.com, and it shows each button plugging both wires into it's socket.
If you want to still use your grounds tied together, you'll need to find the common pin on the connectors. Use a continuity meter if you can, and find the pins that are connected (probably the outer pins, but I'm not sure from here.) That would be your common wire for your controls.
Also found how to connect the LED lights (those do get daisy-chained).