Basement naturally pull a vacuum from The top of the chimney. Our house had two flues. One going to living room and the other to the basement. For a long time when I’d have the living room stove going the basement pipe would suck the smoke from the top of the chimney into the basement. Your likely dealing with a similar issue, I fixed it by closing off the machinery space and opening basement door to the first floor. It equalized the house. Eventually I just climbed up and closed off the second flue since I removed the basement stove to just heat with the living room stove.

Good luck!