In 2005 there was a mid year transition with the throttle body of both the Matrix and the Corolla. Depending on when bought determined which you received.
The “ Drive by wire” design that you have means that there is no independent IAC valve. The idle is set via the ECM.
That being said, certain ECMs of that generation were recalled due to cracks in the circuit board. Reach out to Toyota Care with your VIN to be sure.
Finally, your issue with the high idle at startup most likely points to a leaky Intake Manifold Gasket. Common issue with this generation.
Ask me how I know.