How were the vases fired ?
It's a very difficult question, however, modern scholars solved the process. The most complicated problem was how were the red and black colour produced. Chemical research revealed that elements of black colour is almost same as red colour, reserved part of clay. Since the particles of former are smaller than latter, probably it was skimmed from the dissolved clay. The scholar found that to produce the red and black colour, three stepped firing process was also needed.
In first step, potteries are fired in a kiln with the hole of the chimney opened. Iron in the clay combine with oxygen and become oxide of iron. So the surface of whole body turn to red.

Then the hole of the chimney is closed and the atmosphere of kiln become carbon monoxide, which take oxygen from the clay. So the whole surface turn to black.
In the last process, chimney is opened again and the atmosphere turn to carbon dioxide. Reserved clay turn to red again, though the painted part remain black, because small particles obstruct the combination with oxygen. The experiments revealed that exact process, control of temperature and timing to open and close the chimney, was needed to produce the colour. The scholar expects some organic matter were added to help the reaction. However, it is not clear what was that matter, though ash is the most influential.