A new airtight house does not lose to the chimney. The chimney loses to the range hood.
A fire needs air. An open fireplace pulls a genuinely large volume of it out of the room and up the flue - and that air has to be replaced from somewhere or the fire cannot draw.
In an older house it comes in through the building itself: around sash windows, under doors, through a hundred small gaps. In a house built to current standards it does not, because the whole point of the envelope is that it does not leak. Add a modern range hood moving several hundred cubic feet a minute, a bathroom fan and a dryer, and the house is at negative pressure. The fireplace becomes the largest opening in the building, and air comes down it, carrying smoke with it.
This is now the most common cause of spilling we find in Box Elder, and it will get more common as the new subdivisions fill. It is not a chimney fault and no chimney work will fix it.
Light the fire. Once it is spilling, crack a window on the far side of the house by two inches. If the smoke pulls back up the flue within a minute, the diagnosis is complete: the house was starving the fire, and everything else is detail.
The permanent version of that cracked window is a dedicated makeup air inlet - a controllable duct that supplies combustion air near the hearth rather than through the rest of the house. Four hundred to twelve hundred dollars depending on the run.
What we will not do is sell you a cap, a taller flue or a new appliance for this. None of them address it, and all three get sold for it regularly.
Tell us what happened and what else runs in the house. That is most of the diagnosis done.
Rather talk it through
If cracking a window fixes it, you already know the answer and we can quote the permanent version.