Alarm Sound with Apple Music

When setting an alarm, there is the option in the Sounds menu that lets you choose any song from your Apple Music library. After setting the song (the song title appears in the "edit alarm" menu), it does not play when the alarm rings. Rather, the default Radar sound plays, which is very unpleasant. If I choose any pre-installed tone from the menu like Apex, it works.

Note: My Apple Music subscription is active and renews every month, so it shouldn't be my subscription causing the problem.