I’m having this same problem. I have an S6 and an S4, and I rotate between them. Even when the one I’m not wearing is not on the charger, the alarm still sounds. I have the watches set to automatically switch, depending on which one I’m wearing, and I don’t see any settings in the sleep app to account for this. I can understand the alarm going off when I’m not wearing it and even when it’s not on the charger, but if I’m wearing the other watch, the one I’m not wearing shouldn’t activate. Often I wake up before my alarm and leave the room, and then the other watch goes off and wakes my partner. I have to assume this is something Apple overlooked or is a bug.
I've been able to figure out a way to stop getting the alarm on the watch that's charging overnight.
Have you been able to figure out a way to stop it, or is this a typo?