Unofficial Skyrim Special Edition Patch

Screenshot 1 After the battle for Fort Greenwall, prior to talking to Tullius to end quest.
Screenshot 2 After Fort Greenwall, after talking to Tullius

There are two things going on here.

First, ownership of the cities/towns (or flags denoting same) don't seem to update right away after a fort battle for the various holds, though the forts themselves update correctly.

Second, when the ownership of the towns/cities does update correctly, the flag for the fort goes away entirely. You can see in the second screenshot that all the forts that started under Imperial control continue to have flags, while all the forts taken from the Stormcloaks have all lost their flags, most obviously the ones near Dawnstar and Riften.

Both of these things remain true all the way through the end of the civil war.