I looked at that closer and these are my thoughts.  Where he jumpered from "I" to "L" is where I see what you are suggesting.  "I" is input power for the dry contact relay.  "L" is power to the device itself.  L should be hooked in before the stop switch.  "I" should get power from after the switch AND in the device configuration it should be configured to default to "OFF" or "Open" when the device is rebooted.