Good call checking those chirp settings! @glucas I recommend checking in your Alarm Alerts section of the Ring app. From the dashboard go to menu > settings > Alarm alerts.
Another great place to change this is on the Motion Detector page in the Ring app. From the Ring app menu, select devices and view your Alarm devices. Select your Motion Detector and on the next page you should see a Motion Alerts toggle. Toggling this off should obtain what you are looking for. Feel free to let us know how this goes! 