Make sure that in Apple Watch App -> Notifications -> all of the apps are checked to send notifications.
If this is already the case, you won't get a notification on your wrist if your iPhone screen is activated. Basically, if it thinks you saw the notification on your iPhone, it won't bother your wrist (at least it does this for me. It seems like everyone's watch works slightly differently...)
yep, for example, you are using your phone, or even just the screen is lit up, and you receive a text. there will be a pop-up bar on top of the iPhone. then watch/iphone assumes you see it on your phone and will not give you an alert on the watch
plus, some notification on iPhone has sound and vibration, but does not pop up. like mail for example, by default it has badge, sound, but no alert. in that case you will not receive anything on your apple watch
simply put, apple watch just displays whatever ALERT (not necessarily notification, but alert, when you go to your iPhone's setting --> notification and you will understand the difference), that is not yet displayed on your iPhone (i.e., when iPhone is on lock screen).
----------
My friend had the same issue with texts not appearing on his watch. Try to send a text and see if it syncs.
it sometimes takes a while for the notification to be pushed to the watch. the watch has to be activated, establish connection, and then push all data over. it takes time, especially when it's been a while since last notification.
----------
I found that i had to use Custom as oppose to mirror my iPhone. When you select custom you will see more alert options, such as show alert, sound and haptic.
Watch app>notifications>messages>custom.
you sure you have ALERT (not notification) turned on for that specific app on your iPhone?