The sensor is on the control , The control only reads the temperature around it not the temperature next room. When the fan is ON because the circulation or the air, the temperature is more even from room to room. When the fan is auto , it is only on when the heat is on. Other room's temperature could be higher or lower than the room which control is in.
Usually you put fan on auto first then try to open or close the register(出风口) to adjust each room's temperature. If it is enough, you can keep the fan at auto. If there is still some room being too cold or too hot, put the fan at on would makes things better.