Alarm ringing on both iPhone and Watch simultaneously

I have an alarm set on my iPhone through the Clock app. When the alarm rings, both my Watch and my iPhone are simultaneously ringing/vibrating. It seems that only one device should ring, much like how other alerts and notifications work between the two devices:

• If I'm wearing the Watch and it's unlocked, only my Watch should ring.
• If I'm not wearing my Watch, then only my iPhone should ring.

I think the above is how alarms used to work, but now both my devices are consistently ringing. I already tried restarting both devices and the issue persists. Next, I'll try re-pairing the devices, but that's some work and wanted to check here first. Is anyone else having this same problem?