Automatic only reports Check Engine Light (CEL) information and generally not other dashboard notifications (if there are additional lights), e.g. Maintenance lights, tire pressure, air bags, oil pressure lights.
This is because Automatic can only read and interpret any generic "P" class OBD II code given by the car. These codes are related to emissions of the car, which generally involve your engine. The app will not tell you when any of the other dashboard lights are on, only when the CEL is on. Most other lights are manufacturer-specific and not available to Automatic.
If you do see any additional lights go on, please take it to an authorized repair shop so that they can diagnose the problem.
To learn more about your vehicle's "Check Engine" light, check out this blog post.