Today I installed iOS 12 on my iPhone and also wanted to install watchOS 5 on my watch (series 1), but after installing the public beta profile, the software update keeps saying "Software is up to date". What's going on?
This is where common sense comes in. The profile says iOS and not watchOS. Through the iPhone is the only way to install a profile to the Watch. Without the iPhone or iPad, the Watch is useless without a paired device. If you install iOS profile on the Watch is basically useless since it’s not the right profile. It has to be a watchOS profile. WatchOS developer profile is installed to the Watch this way. You can even install tvOS profile on your iPhone so it doesn’t mean you can get tvOS beta on your iPhone.
Sums it up:
iOS for iPhone/iPad
WatchOS for Apple Watch
Installing the wrong profile on the wrong device will not trigger the right update.