How does phone 'S' interaction work over 3G?

I don't own a Gear S yet, so apologies if the answer to this is obvious from using the device. I've read numerous reviews and a few pages back in the history here without finding what I'm looking for..

I'm curious about the specifics of how the paired smartphone and the Gear S communicate over the 3G network, and whether any carrier "shenanigans" are involved. For example when an SMS arrives on the smartphone does it send a notification to the watch via TCP/IP? If I reply on the watch is the reply relayed through the smartphone the same way? I don't think it can work this way because if so the smartphone would need to be powered up and connected to the carrier network for the "I only carry my Gear S when I go out to dinner" use-case. However, if the SMS is sent by the carrier network directly to the Gear S, that implies the carrier has to know about the device and it has to be somehow associated with the "line" assigned to the smartphone. If this were the case then the user reports of "cross-carrier" operation (smartphone on VZW, Gear S on ATT for example) couldn't work.

Since I can't deduce how it works from the feature set, it would be great if someone who knows the scoop could point me in the right direction. Thanks.