If you are referring to downloads from the WSUS server by the WUAgent on any given client - that you'd like them to use the fully qualified name - this is not something that the EminentWare Extension Packs can control. The WUAgent will be given URLs based on the simple hostname of the WSUS server, so the client systems will need to be able to properly resolve that simple hostname through DNS/DHCP.
If you are dealing with cross-domain WSUS registrations, you can register the WSUS server with the FQDN in the ExtPack by going to Update Services and opening the Update Services Registration Management wizard, selecting your WSUS server, and specifying the FQDN in the "Connection Name" field.
Nevermind, the URI displayed in your software seems to be ignored by the client when downloading. Since the patching server is configured using the FQDN on the client, it's using that as part of the download string instead. I didn't bother to actually test it and went by what your software was reporting.
In the windowsupdate.log file it clearly shows the download URL using the FQDN.