Aphyosemion, I think what you discovered in your tank is not blackworm, but rather tubifex that somehow managed to find its way to your tank.
Blackworm is midge fly larvae. It won't multiply on its own in the worm stage, nor would blackworm lay eggs for the same reason.
Tubifex on the other hand is usually brigher red in color, shorter and more engergetic in appearance. Tubifex is a true aquatic worm, it's worm as larvae, and it's worm at sexual maturity.