I suspect you are burning wood pellets and they take forever to burnout and stop making smoke. There isn't enough heat produced to keep the exhaust fan on but the darn pellets keep making smoke. Corn doesn't do that.
Like "the bone" says if your hopper lid has a safety switch that turns off the auger when the lid is up, that should stopped the auger from feeding pellets and keep the exhaust fan on long enough for the fire to burn completely out. If there isn't a switch in the auger circuit that will turn the auger off, add one.