We’re currently working on integrating the alt text features from the module into the core of Omeka S, so as Megan says, definitely do reach out if there are problems, missing features, things like that.
The Alt Text module lets you either manually specify alt text in a separate text field, or choose a piece of metadata to automatically use as the alt text. Both the input for setting manual text and the metadata values that will be used are those of the Media, not the Item.
If there’s either kind of alt text specified for an image Media, it should automatically be used, unless the theme is written to manually supply an alt attribute, in which case that will be used instead.