How long have you had the Watch? Did you just get it today? What have other notifications been doing (besides text messages and emails)? I've had short stints where perhaps the Bluetooth connection was not communicating optimally and notifications will buzz in on my phone in my pocket prior to the Watch. This usually won't last long after I play around with one or the other or both for a little bit (actually just playing around with them- not adjusting any settings, just waking them up and exploring around some). I really don't know if me getting the juices flowing in either device does anything, could easily be correlation.
Guessing that's not really your issue the way you describe it, but if you're certain that you've managed setting up the notifications properly between both devices, I'm not quite sure what the issue would be here.