No wake alarm on watch when iPhone is awake

I use the haptic wake alarm set by Sleep as my alarm clock and I missed an early appointment this morning because the alarm went off on my iPhone (which was in another room) instead of my watch.

I use an app that controls a Harmony Hub, which controls my home entertainment centre and the app has an option to prevent the phone from sleeping while it is in use. Last night I turned off the TV etc. but left the app open, which kept the phone awake all night.

I'm assuming that, seeing the phone as awake, Sleep assumed I was using it and sent the alarm to the phone instead of the watch. Is there a way to make the alarm go off on the watch regardless of whether the phone is asleep or awake?