A secondary air problem is not always caused by the secondary air system. With the engine cold, start engine. If the secondary air pump runs and can be heard, the issue may be in the airflow control side.
If the turbo bypass or over-run cut off solenoid valve does not hold vacuum it can cause a secondary air fault. It shares a manifold vacuum source with the secondary air combination valve and under certain conditions prohibits the combination valve from opening. This will set a P0411 secondary air incorrect flow code.
Part # 06A 145 701N - Located just behind and to the left of the combination valve. Test the solenoid using a handheld vacuum pump. The valve should hold vacuum.