Zones do not short to common to operate. Instead they apply 24VAC to the output. I'm sure Rachio is using triaks, so you can't use OHM meter on a line without having a VALVE connected. To test connected zone, use an AC voltmeter to make sure that an active zone gets 24 VAC with the valve connected. If you do an OHM test while the zone is OFF, you will get an impedance across your water valve, allowing you to test that valve connections. If you get an open circuit across the valve, you need to make sure that the valve side connections are good and none have came loose.
In any case test AC voltage between an active zone terminal and C terminal, you should get about 24VAC. If you don't have a valve connected, DO NOT test AC amperage, rachio is not designed for low impedance high amperage loads (type of load a multimeter testing a current would represent), make sure you are using some impedance (such as a valve or a 10k+ resistor) between zone terminal and common and use voltage test to verify operation.