Thank you for your post.
I don't have a clear-cut answer why FileMaker Server is not closing out that connection. FileMaker Server should not allow the same customer to log in twice using the same license key.
It seems that Admin Console is not updating properly. Is it possible that the client originally crashed using FileMaker Pro? These are merely guesses.
Reboot the server, and please keep an eye out for this type of occurrence. Try to write down everything that happened prior to this multiple display of the same client.
Sorry I can't be more definitive.
It's been a fairly common thing to find the Admin Console not upating things like it should. In most cases, I've been able to simply restart the console (rather than the database server) to fix this. I'd try this first as this won't interfere with people who are trying to use the database.