Just to be clear, literally you can get the secondary air system to clear in the PCM. Start the car cold, let the air pump kick on and cycle until you dont hear it, turn off car, repeat 3-4 times. Your not letting the car warm up, just letting the pump run. If the air system has a fault it will put your check engine light right back on.
My advice, if brand new pump, pull the hose from the air filter housing it goes down to the pump. then pressurize it with a shop vac or air compressor. Spray down all hoses to secondary air pump up to the secondary air check valve with soapy water, if leaks, repair as applicable if leaks. If no leaks, I would pull off the secondary air check valve, and clean every bit of carbon out I could and put back on. If no changes, then its either a faulty valve, wiring, or alternative you got a faulty pump out the box. Hope you figure it out.