As @DLane has already outlined your best bet is to use one Dual Throw relay, it does not matter if it is a Single Pole (SPDT) or Dual Pole (DPDT), though for 24VAC DPDT relays are more common.
Here is a visual schematic of how one DPDT relay can be used to control your pump relay:
Note that wires shown going into the hunter pump relay are connected to control wires (polarity does not matter), not the pump terminals.
Schematic is drawn so that relay orientation has pins 7 and 8 at the bottom. In this case I've used this relay (link), though if you ended up using a different relay, just follow @DLane's instructions and you should be alright.
Let us know how it will all turn out.
P.S. For anyone else joining us, this solutions does not require that a second controller be a hunter controller. It will just as well work between two rachio controllers or in combination with controller from any other manufacturer (as long a they use 24V AC power supplies). This is a significantly more affordable solution when compared to the official how-to article (link).