My understanding is that it has to do with the partial pressure gradient, in other words, there is such a much higher concentration of CO2 in the tire after you inflate it than in the ambient air that the CO2 tries to escape to equilibrate that imbalance.

When you pump up with air, you create a gradient due to the higher pressure, but it's not as extreme as the gradient between pressurized 100% CO2 and the partial pressure of ambient CO2 in the atmosphere.

I carry a pump and CO2 as well, the best technique I've encountered is to actually blow the tube up with your mouth first, then CO2, then top it off to rideable pressure with the pump, because even two CO2 cartridges won't get a 700x32 tire, for example, fully inflated, and for a bigger tire you might need three or more.

For a flat in daylight and I'm in no hurry, I would patch and pump and not even use the CO2.

The CO2 cartridge alone I would use if I got a flat in the dark and in the rain or if I were in a real hurry, then I would just use CO2 to get it rideable, not worry about topping it off, and get home or to the destination or to shelter ASAP.

Nighttime, or sketchy area with many miles to go and no close shelter/alternative is when I would inflate by mouth, then CO2, then pump as above.