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

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.