I am so confused by this, probably because I don't have a traditional XMPP client to base experience off of. Could you log in to, say, pidgin, and do this? I guess I'm not understanding the relationship between the log in name "Felderburg@chat.cohtitan.com" and how you connect to other private servers, or a JID (whatever that is).
"Connect to other private servers" is probably where you're being tripped up. The idea is that, by way of example, you'd be connected to Titan using your Felderburg@chat.cohtitan.com account, and be connected to chat.cohtitan.com. However, your friend Godzilla could connect to Godzilla@chat.monsterisland.com and be running on that private server. Hypothetically speaking, if Godzilla was in your friends list or vice versa and you wanted to zone into the Atlas Park running on MonsterIsland to see him, you could instruct Paragon Chat to join atlaspark@chat.monsterisland.com (plus the meta channel) and you'd appear there. You wouldn't need an account on Monster Island nor would you need to "log into" Monster Island. Paragon Chat would send those commands to chat.cohtitan.com and chat.cohtitan.com would route them to chat.monsterisland.com. If Titan and Monster Island are configured correctly, they will route those messages between each other seamlessly and you'd be in the atlaspark XMPP room, and your character would appear within that version of Atlas Park.
To make this work, Titan and Monster Island have to be internet reachable, and be configured to accept those connections. In so-called open federations, XMPP servers are basically configured to allow anyone to connect to them, so if Titan was configured that way, any private server could also be configured that way and allow anyone from them to reach Titan and vice versa simply by setting the right addresses in their messages - the XMPP servers would do the rest for you. In more tightly controlled conventional federations, servers have access lists and sometimes authentication that is set up so that approved servers can connect.
You could always ask for an account on Monster Island and use that in your Paragon Chat program: Paragon Chat will then connect you *directly* to Monster Island and you'd by default see everything there and only there. But with server to server connections, everyone could connect to their own "home" server and still enter any City of Heroes zone on any other server so long as they are configured to allow that.
This requires extra code in Paragon Chat to happen, but mostly housekeeping code to actually attempt to do it at all: XMPP itself (more specifically the XMPP servers) does the work. But think about it this way: when you mapmove to Atlas Park, what's really happening is that Paragon Chat is converting that into a set of XMPP directives to join atlaspark@chat.cohtitan.com. I presume that Paragon Chat basically assumes that the Atlas Park you want to join is on chat.cohtitan.com because that's the server you're connected to. If you were connected to something else, it would automatically assume you meant atlaspark@whatever. But it doesn't *have* to assume that. Paragon Chat could allow you to mapmove to Atlas Park @ Anywhere On Earth. If that server was reachable from chat.cohtitan.com, acknowledging things like latency, it would just work. So if you had a friend Godzilla@chat.monsterisland.com and there was a Paragon Chat command called "join_friend Godzilla" Paragon Chat could query** to find out which room/zone Godzilla was in (which doesn't even have to be on Monster Island, keep in mind) and then execute the commands to join that room. Then you'd be where he was, period.
** Masking some technical details here, like subscriptions