If the contagion passes through the blood, that would have rendered the blood-drinking Red Court particularly susceptible. We know the Reds called up Outsiders to attack the Council, and who knows how far the infection had spread by that point (assuming Arianna and Bianca were in fact infected). Nicodemus---who, based on his conversations with Harry in Small Favor, definitely seems clued in about the contagion---mentioned to Harry that he wanted the Red Court to be destroyed, but never specified why; if he knew Nemesis was transferred via blood, he would have known the Red Court (despite its Fallen-friendly MO of causing harm) was too big a danger to be allowed to survive.