The AIR pump can run for a maximum of 4 minutes after cold startup, turning off once the PCM switches to closed loop operation. It will also turn off if engine speed exceeds 2825 RPM, or if temperature is below 14°f.
During the brief time the pump is running, the 02 sensors are expected to read leaner, this is how the PCM monitors the AIR system function, and how it can generate trouble codes if the pump or a check valve fails.
The 02 sensors during this time of open loop warm-up are not contributing to fuel trims. That only occurs once in closed loop mode, when the AIR pump is switched off.