Boy, that sounds like a very specific feature to ask of Rachio. Not sure there is really any sensor input on Rachio that would allow for it to then kick a pump on. Seems like this might be something that needs to be engineered separately with some float switches and relays. When Rachio kicks on, force it to always kick the pump on and leave it up to a relay to make the decision if the water level is high enough to warrant it. Problem then is, when there is no water in the reservoir, what happens next, are you also plumbing in a shut-off valve from your main water line that opens up only when the reservoir is dry? Not a simple task, and way more than Rachio can, or should handle.
My advice would be to set up your reservoir system with a float valve that is plumbed into your water line so that if/when it falls below a set level, it will fill with tap water. You will of course always have a pump running when your sprinklers are running.