SW+ Alerts includes "Critical Alerts" technology, which means that warnings that require immediate action to protect life and property (Tornado Warnings and Severe Thunderstorm Warnings) will override devices that are silenced, muted, or on Do Not Disturb, sending a loud "wake-me-up" audio tone. Please see this article for more detail and how to ensure Critical Alerts are enabled.
Please see this article on how to override Do Not Disturb on your Android device. While the app will not sound over silent or vibrate settings, you may override Do Not Disturb. This is not automatic and each user must configure this on their own device, per Google requirements!