I spent a lot of time working through this issue on my new Lumia 950. I wanted different sounds for each of my email accounts but I did not want banners. For this reason, in the In [email account]/Settings/Notifications I did not check the "Show a Notification Banner" but I did check "Play a Sound". Seems intuitive...
When I checked both boxes, sounds started working. Apparently the way to disable banners is to just do it in the general Notification Center on an app by app basis...not so intuitive.
Now, my remaining notification issue is to figure out why some of my apps are not listed in the Notification Center....