Working as Intended. Paragon Chat is decentralized. That means your characters reside locally, not on the Titan Network chat server. Which is exactly as it sounds: all the Titan Network server does is handle chat transmissions. Everything else is up to your system.
If you want to create the characters on one computer and have the other one match, you can copy the database to the 2nd computer to make them match:
On the donor computer - Open Paragon Chat, and click the blue folder. Open "Database" and copy the ParagonChat.db file. Save it on a flash drive or a network location you can reach. On the recipient computer do the same thing except you'll copy ParagonChat.db to the system.
Also, a periodic backup of ParagonChat.db is a good idea, if you are active in capturing Badges or have a large roster of characters to save. You can also use the tailor in Icon to save .costume files of your costumes as well.
The "Local Account" screen has a username where characters are stored on the database. You can have it match your Titan Account name, or enter another one. Each username has 48 character slots (the game imposed maximum per server.) So if you want another 48 if those fill up, enter another Local Account name (in your case, like KrazieFox2) and another 48 slots are available. Reenter the original Local Account name to return to your prior 48. Don't worry if you forget what Local Account names you've used, open Paragon Chat and instead of logging in, click the Gear Icon, then Database Browser. You'll see all the Local Names there.
In this manner, you can have as many characters as you like.