@Lynn25 - you have two options:
For both options a pump start relay (Orbit or similar from Home Depot or Lowe’s) will be needed to turn on the pump and an external enclosure will be needed for the Rachio (unless it is being installed inside and the field wires run through the wall to the current location).
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The Rachio M and C terminals will make the connection to the pump start relay. Create your three zones in the Rachio app using a Fixed type schedule and specifying a pump start relay is attached and a recovery delay between zones. There won’t be any connections to the zones in the Rachio. It will turn on the pump for each zone. The Flex Daily type schedule is incompatible with this setup.
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Replace the indexing valve with a 3 valve gang (Orbit makes one). This time the zones on the Rachio will be attached to the solenoids in the valve gang along with a wire to a C(ommon) terminal. Again the M terminal will be connected to the pump start relay along with a wire to the C(terminal). With this setup one can use the Flex Daily type schedule if desired or run a specified zone.
There are numerous posts with before and after pictures where users have replaced an indexing valve and Intermatic timer with individual valves and Rachio.
Edit → here is one of the posts documenting a Intermatic to Rachio w/ individual valves conversion → Installation: Figuring Out the Wires?