If you use distributed monitoring and replicate the configuration from the central site to all the remote sites, then you would create the contact groups and memberships only on the central site. In fact, you would literally configure everything on the central site and nothing on the remote sites.
Honestly, I have no idea what to do if you do NOT replicate the configuration. I don’t know which configuration then wins.
Beware: Do not change the replication setting to “Push…” without knowing what you do, because then the complete configuration of the remote sites gets overwritten with the central site’s configuration.