Minor UI issue, could be a bug, could be WAI, might have been overlooked. If you select a fleet in the Naval Organization window, then select a ship in another fleet, and then click on the Fleet tab, it will show the fleet information of the original fleet you first selected, and not the fleet of the new ship you selected. Based on behavior, I believe the Fleet tab is only being updated when you actually select a new fleet. If not intended then you may want to consider it, imo it would make sense to update the fleet tab to show the information of whatever fleet the current ship belongs to.
SJW: It is a 'bug', but I am going to leave it alone for now and fix when I have a lot of time to deal with the resultant consequences of changing it.