I see a possible error in your statement about the 24V. You stated a + and - which is a DC voltage statement. The Rachio will only send an AC voltage output. This may only be a minor misconception but understood.
Secondly, you may have a pressure switch on your pump which may be calling for the pump to come on during a lower pressure situation.
I would double check and make sure the controller is off when connecting it to the relay. Then test it with the master valve output to see if it works only from the desire output at the appropriate time.