Considering that there are enough zones on the old controller, I would recommend hooking up top row of wires to unused zones 13 through 24. Prior to switching over try running every zone and note if any are unused. We had other users with similar controllers to yours. Seems that abundance of terminals is an easy way to terminate any unused zones (in case more zones are coming in than are actually needed).
You are better off identifying the wires that are actually needed and leaving unused wires disconnected. In case you do with to proceed with twist and hookup method, than I recommend you use a wire nuts and not force a thick twisted pair into the Rachio’s terminals.
Above topic may provide some guidance as to what you are facing. Let us know if you run into any issues 
Welcome to the community, enjoy your updated Rachio 