I think you missed the point. The cooling fan for charging should cut out soon after 100% charge is reached and the battery is at a reasonable temp. A lot of people but not all find this does not happen and the fan stays on after the battery is charged, this wastes electricity until you unplug from the mains. Then is stops as you say.
Now if you unplug before the battery is cool and run the car straight away the fan will cut back in. You can also make the cooling fan cut in by driving hard in hot climates - not here in the uK