From: My Mother, although my Father had some small part.
I think the key might be the order to upgrade. I have had tender type ships with supplies on board not unload when I moved them between ports etc,. but I always leave them set to "Do Not Upgrade".
Someone posted recently that if a tender was set to "Upgrade Allowed", it would start unloading supply while it was disbanded in port. I haven't seen that myself, but that is what I understood from the discussion. Normally, when I want to upgrade a tender with supplies on it, I put it in a TF, dock it, set it to unload and auto-disband, and of course set "Upgrade Allowed".
Yes, the ships will slowly unload in port before the upgrade. It is actually quicker to put it in a TF, dock it, then unload it with the TF disbanding, and the upgrade set to "Yes" so it will upgrade. Once the ship has started the upgrade and/or repairs, you can go to the repair screen then select "Load Tenders" and the ships will load.
Seek peace but keep your gun handy.
I'm not a complete idiot, some parts are missing!
“Illegitemus non carborundum est (“Don’t let the bastards grind you down”).”
― Julia Child