Photoshop is most often used as an artistic tool, not as a means to scientifically reproduce the precise colors and tones in an image. In fact, for most typical photographic uses, no one would ever prefer a strictly accurate reproduction of a scene to the modified renderings that have been associated with photography for the past century.
Just like it would be absurd to tell a painter that cerulean blue is the "correct" pigment for the waters off of a small list of Caribbean islands when looking north on a clear day at noon, it would be equally absurd to tell you that a particular auto correction method is "the correct one". Use the options to find a look that pleases you, or at least seems to be the closest to your memory of the scene.
That being said, there also are scientific, forensic, product photography, and other uses of Photoshop / ACR that demand absolutely precise color and tonal renditions. This is a very large and deep field. It demands camera, monitor and printer calibrations, highly controlled lighting, as well as strict control of the overall workflow, use of well established color standards (eg, Pantone), etc. Suffice it to say that no one operating under such constraints would EVER dream of using an auto-correct option for such uses.
HTH,
Tom M