I’ve reproduced this on three separate computers, each running Precise.

Steps to reproduce:
1. Start Software Center.
2. From the File menu, choose Sync Between Computers…
3. From the registration window, choose to login to you existing account. Enter your credentials and continue forward.

What happens:
In addition to the window saying you’re now signed in, you also get the registration window. Sync is not available in the main window.

What I expect to happen:
To have only the successful sign-in window appear (i.e. not the registration window again) and have sync working in the main window.

Workaround:
Start the Sync procedure again. Repeat steps 1.-3. above. This time it works as I expect it to: the registration window doesn’t re-appear after entering my credentials, and I get the sync view in the main window.