I have never had a back draft, caused by closing the MPD, ... that I'm aware of.
If it were my situation, I'd ask myself: If the chimney was high enough? Is something else pulling air from the house, such as the furnace or an exhaust fan, coming on? I witnessed my upstairs curtains, suck in (in the fall, with window open), when my furnace started, in my 1880's house, which shouldn't be that air tight. After that, I added an outside air source for the furnace. I now also, have outside air source for the coal stove and the fireplace.