On my platform: Windows 7 Pro, Tixati v2.31 does NOT maintain any TCP traffic after exit. If you have set your options on "Close" to "Hide In System TaskTray" it will remain running in the background. But if you actually "Exit" it should be gone.
If you had lots of connections on Exit, then those will keep trying to connect to your Tixati port for a while but no one will be home to answer the calls.
http://imgur.com/1KUXnP0