The auto rain delay and rain sensor are two separate things. ‘Auto rain delay’ uses weather data, so it can trigger rain delay without any rain sensor physically connected to the controller.
The ‘Rain Sensor’ refers to ‘Attached Sensor Type’ — meaning a physical rain sensor connected to the sensor port. If you choose Rain Sensor, the controller will stop watering if the rain sensor is activated. In your case, if seems you have selected rain sensor and selected ‘Normally Closed’ (because the Normally Open checkbox is not on). If you do so, and you don’t actually have a normally closed sensor connected to the controller, it will think the sensor is activated at all times, hence no watering will occur.
Generally you will use either ‘Auto rain delay’ (if you don’t have a physical sensor, hence relying on weather data), or ‘Rain sensor’. It’s not common to use both.