The auto-sort "button" is a checkbox in the config screen somewhere. Don't get your hopes up. It really doesn't do very much.

Honestly... I actually have no idea what it accomplishes. I've had it enabled from the get-go. I do know that it only does whatever it does when you actually receive an item, but I couldn't tell you the difference between the behavior with the box checked and without. Perhaps this is why potions and food always go on inventory tab 3 (except when it's full)? My items do stack themselves, so maybe that's it.

/shrug

My inventory is still a hot mess. Materia all over the place, crafting mats scattered around like whoa.