NSUserActivity didn't forward notifications, it just provided a way to move whatever you were doing on your other Apple devices to the one you're currently using and only covered things that the dev specifically implemented.
Oh interesting! Does it mean that the content of these forwarded notifications goest through Apple servers then? With no way for the source app to prevent it?
I haven't picked it apart, but if it's like the other Continuity features it all takes place locally over bluetooth and ad-hoc wifi. There's a possibility that their servers are just sending the notifications to the user's Macs in the same push that sends them to the phone though.
This works for all notifications from all apps.