Available starting with iOS 12, Critical Alerts are special notifications that may only be included in an iOS app after being granted special approval by Apple. Critical Alerts bypass the device's mute switch and Do Not Disturb settings, overriding these features with audible alerts for emergency situations.
As of StormWatch+ version 4.1.0, released in 2020, Apple has granted Critical Alerts status to SW+ Alerts. This means that warnings that require immediate action to protect life and property (Tornado Warnings and Severe Thunderstorm Warnings only) will override devices that are silenced, muted, or on Do Not Disturb, sending a loud "wake-me-up" audio tone.
You must have granted the app permission to sound Critical Alerts when you installed the app. To check whether Critical Alerts are enabled, open your device's Settings app, scroll down and tap StormWatch+, then Notifications, then turn ON "Allow Critical Alerts."