What you are describing is quite prevalent in refiring glazed ware at at China paint temperatures. It is often called mildew but it is actually black spotting that occurs on the UNGLAZED surfaces when the clay body has NOT been fired to full maturity. Hence you will normally find it under the work (where it touches the shelf)and footrings. It is not trapped carbon from poor bisqeing. It is mostly found in older pieces that have been around a while. It is carbon being trapped in the open pores of the body and this can be generated from a variety of sources.
The carbon can become reabsorbed and trapped from the media being used so it is more prevalent to occur from oil based mediums than water based mediums. This coupled with poor circulation and ventilation in the kiln during firing allows the pores of the unglazed clay surfaces to reabsorb this new carbon. This carbon can be burnt out with repeated firings especially if the temperature is raised slightly higher. The easy answer to all this is that if you are making things from scratch make sure you fire to the full maturity of the clay or otherwise get a clay that vitrifies at the temperature you want to fire to. Then this problem shouldn't occur. Always make sure you have the lid or door of the kiln slightly ajar in the overglaze firing until at least 650.C This allows the gases generated from the mediums to be dispersed. Always allow plenty of space between the shelves in the kiln during an overglaze firing. Always try to fire to the highest temperature in your overglaze firing depending on your glaze type. eg if using porcelain fire to 800-820.C rather than the lower 760-780.C option. This allows more carbon to burn out. If at all possible fire your pieces lifted OFF the shelf by little wads or pins.
I have attached a small .pdf made from page 125 of "Ceramic Faults and their remedies" by Harry Fraser. This deals with this topic in greater detail and it saves me from having to type it all out.
Black spot.pdf 492.53KB 15 downloads