I believe this falls under the category of "toast notifications"
When I first installed the app (back when it was called Messages+), the pop-up notification would appear containing the name of the sender and a preview of the message content. For some time now, the message content has disappeared, the pop-up simply reports that new content is available.
Is this by design?
According the Windows Store, the app hasn't been updated since 2015, so I'm not sure why/how the feature could have changed.
The app has all notification settings activated.