Yes but to lower NOx the CO2 goes up if they lower temps.

Yep. Lowering temps by adding excess fuel per cycle to lower combustion temps by thermal mass and heat of vaporization. The fuel doesn't ignite because of careful regulation of the throttle plate (and in turbocharging engines, wastegate/sizing) management.

My naturally-aspirated gasoline engine has a third-party flash that lets the throttle plate open much more quickly when you step on the gas. It feels much snappier, but opening the throttle plate too quickly allows excess oxygen to burn the extra fuel, not leaving any for heat reduction, which means there are steep increases in NOx and temperatures during acceleration.