Hello UpstateMike.. you should leave the over the fire air vents closed except when fresh coal is loaded.. not all coal or coal stove instalations will create 'puff-backs' it depends on trapping the gasses, volume of air/gasses and chimney draw..
Leaving the over-fire air open to cure excess draft, or 'tipping the lids' in an old cookstove are bandaid techniques to deal with a too strong draft.. that is what Barometric dampers were designed for.. to limit excess draft to a managable, controlable level..
Have you installed a manometer in your instalation so you can see the actual draft?? It is much easier to figure out what is happening when you have some instruments to read.. instead of waiting to see the results of under or over draft, heat etc..
Take care,, Greg L