Auto gets the cabin to the desired temperature... eventually.
It maintains the cabin at that temperature... somehow.
And most of the time it works.... reasonably well.
You'd think that the greater the temperature differential, the higher the fan speed. But it isn't always like that. My 2 previous cars they both had an OPTION of imposing manual fan control on top of the automatic temperature setting, which sometimes was necessary, because getting into a really hot cabin sometimes the fan was barely wheezing; or when the car is already chill, the AC decides to blast an arctic storm.
But for the most part auto climate control in most cars work well.
Though my favorite system was this Honda. All the controls were literally at my finger tips with hands in the standard driving position. The cabin was small so extremely easy to bring to temperature. And the 7 stage fan allowed you to set just the perfect speed.