Is that an issue or a feature?
With my Pebble, it just mirrors the notifications. I still get the sound/vibration on my phone, but I can look at it on my watch. I was hoping my Apple Watch would do the same thing. I don't really want it to replace my phone notifications... I just want a faster way to glance, and see if I should bother getting my phone out to acknowledge it.
its an issue. Per the Apple Site, the notifications will only go to the watch when the phone is locked (screen off). when the phone is unlocked (screen on) the notifications will go only to the phone.