The stone is extremely porous! That's how it produces the incredibly crispy crusts we all love. Unfortunately, that means it absorbs oils as well as water. If your food has a lot of oil in it or if the oils spill on the stone, they will be absorbed. This could cause smoking during cooking and staining. This is normal and will not impact the use of your stone.
It is best that you do not use oil as a non-sticking agent when cooking on your stone. You can liberally dust the hot pizza stone with cornmeal before you add your pizza, or use parchment paper.