Notifications (Sounds, Haptics and Banners)
Apart from actual phone calls which ring on both by default, the Sounds and haptic notifications and banners for messages etc follow these rules…
~ If the phone is in use (open) then you get notifications on the phone. Messages and Mail still appear silently on the Watch in the relevant app without banner..
~ If the phone is locked you get notifications on the Watch. If you have notifications set for iPhone Lock Screen or Notification center they still go to the phone, but silently without banner.
~ If you go into each notification type and use Custom and disallow notifications the alerts and banners go to the phone always and not to the Watch
Notifications on your Apple Watch - Apple Support