At Layer 1 traffic on this network backhauls to a ground station nearby. On some constellations the ground station may be elsewhere, as traffic hops between the satellites before getting to earth. Egress to the Internet is then managed through the supplier's network based on business rules.

Often that is, indeed, regional peering points. But for Chinese airlines the data is carried back to China to pass through the Great Firewall, even if the satellite ground link is in the USA. Some crazy IP engineering involved.