You could be getting a downdraft through the ashpit, but it is not likely. Do you have another flue in the same stack or another chimney close by that goes to the basement (for the water heater, boiler/furnace etc.)? If you do, it is likely that a number of factors are at play together 1. you have a chimney that is too short in relation to the home - the highest part of the chimney is lower than the highest INTERIOR space of the home. 2. The house is relatively tight. 3. The chimney is an exterior chimney that remains relatively cold (and coupled with the height being too short especially) leads to an easy downdraft through the basement flue. The smoke rises up the fireplace flue and back down through the boiler/furnace/water heater flue that leads to the basement. It is also possible that, providing the chimney is relatively short, your smoke leaves the fireplace chimney and flows down around the downwind side of the home; this side of the home as a basement window that is partially open or a vent that is open allowing smoke-laden air back into the basement.