AIR pumps were originally added to encourage the combustion reaction to continue in the exhaust manifold. The converter was filled with platinum beads. Baffles directed exhaust gas through and around the beads. These cats took much longer to come up to temp than today's converters. So the pump would operate at low temperatures before the cat lit off. The heat would be carried to the cat to warm up the beads while the exhaust was cleaner than if there was no AIR system. As the beads warmed, the fuel air reaction would begin in the converter and after a time, the AIR system would be deactivated. I have to admit that I don't know if AIR is activated today to supply O2 during rich conditions. I do know that it's still used after startup, primarily when engine temp is low, just as it was years ago. I also know that activating AIR when the exhaust is extremely rich and warm can result in sudden, violent reaction throughout the exhaust system, also known as "Boom!"