I have this same problem when receiving Mail and have filed a bug report...
When I receive mail while my iPhone is sleeping, I get a notification on my Apple Watch. But that notification is not enough to alert me that mail has arrived. This causes me to miss timely emails (important for my business)
The problem is that when the iPhone is sleeping (always sleeping when it is in my case on my belt), the iPhone will not vibrate or play a sound. Instead it uses the Apple watch to notify me. While this might seem like a clever idea, it is very bad because it does not work.
The haptic pulse is not strong enough (even when turned up all the way) to alert me.
SOLUTION: Allow users an option to let the iPhone vibrate and play a sound when mail arrives while wearing an Apple Watch with mail notification turned on. (You need both the Apple Watch and iPhone notifications at the same time).
I have missed enough important email notifications to warrant my turning off notifications for Mail on my Apple Watch. That way my iPhone will notify me when mail comes in.
I will leave the setting that way for now. But it defeats the main reason that I wanted an Apple Watch. I want to be able to simply raise my wrist when I hear an email arrive to see if I need to pull my iPhone out of my case to read the mail.
Apple could fix this in the Apple Watch app in Notifications / Mail / Custom
by having two options instead of one. The two options would be:
Show Alerts on Apple Watch Only
Show Alerts on Apple Watch and iPhone.