The refill behaviour just isn't practical atm and pretty much everyone turns it off after seeing some carved wood in the furnace.
While I don't think that fixing this needs to be a priority, it's unnecessary for every newbie to run into the issue. The default behaviour should just be 'off' until you get around to fixing it.
Cheers o/
Also, the firewood refill by companions should be restricted to bundles of wood, excluding special woods. That's not a perfect solution but a perfectly workable stop-gap for now. Anything crafted and special wood has no business being thrown in the furnace.