The simulation cluster, Tranquility, sets the access control lists on the chat channels on the chat server, since it is authoritative on where you are located, in what corporation you are, etc. When you move from one solarsystem A to another B, it will delete your access to local A (and the chat server will then kick you out of that channel) and grant you access to local B and your client will then join local B.
To ensure everyone is updated then the simulation cluster further announces your departure from local A and announces your arrival to local B. The other clients in those locations therefore don’t depend on the chat channel membership list for your presence but rather have that information as well directly from the simulation cluster.