Apple did a bit of a butcher job with the overlapping of text to speech with the Apple Music player in iOS 13 and it is still broken in all the patches up to 13.1.2. As a workaround until they figure it out... you can:
- try different voices (the behavior is different with each).
- try to either completely overlap the song and announcement or keep them from overlapping at all (one starting while the other is playing is the broken piece)
- purchase the specific songs you use for walk ups. (Non-Apple music songs do not use the problem player)
- use an alternate Apple device on iOS 12 or earlier.
