Depends on how the AH is set up. Some fans will continue to run for a while even if you turn the fan off or dismount the stat but that is usually only for a very short time ( minute or two). If you can not turn the fan off at all by the switch or dismounting the stat your relay is either stuck or your low voltage is somehow connected to your call wire for the fan feeding constant control voltage to the relay.
"I am for doing good to the poor, but I differ in opinion of the means. I think the best way of doing good to the poor, is not making them easy in poverty, but leading or driving them out of it."
Benjamin Franklin, 1766