The watch is supposed to preempt the iPhone for notifications when it's attached to your wrist, and switch back to the iPhone when it's not connected. This is a battery saving feature.
If you're missing notifications you've set up, you could try selecting the stronger haptic pulse to see if that helps. Your watch is properly attached if you're not having to repeatedly unlock it with your passcode. If your wrist is extra hairy, it may also be damping the haptic pulse.