Once they've set at a port, that will be their home port. If its out of range you have to control-click to reset the home port (since otherwise they just dock but in the future will repair and supply from the original home port).
I've done it quite a few times, which is why I brought up the lack of any explanation for this feature. They do need to move to the port though, as the tooltip points out ("ctrl + right-click to cancel mission, and move to that naval base").
At this point I'm thinking their
fuel distribution system is broken in some not-obvious way not discernable through the the supply system API's in the base game.
To put something of a lie to your claim above, I have 2
fleetstaskforces on hold orders in a level 8 navy base with 10 infrastructure, the port is not blockaded and the army units stationed there are supplied normally. The supply convoys for that island have never been attacked, let along being sunk.
But the Supply area map mode is reporting naval supply demand on the island is 0, even as the two taskforces are complaining about being in low (fuel) supply. Some more screwing around with the one task force(moved it to reserve status) magically fixed its supply problem, but it took until the next day for the new supply source to be reflected on the supply map(so I guess it is updated on a new day at 0100)
It looks almost like the
fleet determines the home port for the task force now, but it provides no means to control that selection. To further confirm this "feature" I subsequently took the second task force and moved it between fleets while in that same port. Sure enough, depending on which fleet I placed the task force in, the task force would go from in supply to being low on supply.
It looks like they have abstracted naval supply in some way that
the fleet determines where your ship is being supplied from. Going to mess with it some more, but the meta on this is all kinds of screwed up in terms of the micro that players will have to go through in terms of managing what auto-magic the game is doing to where their fleets are getting supplied from. (and having to reshuffle fleet compositions to adjust for whatever limited ability such shuffling allows)