Plugin by default works with two deafult WordPress taxonomies 'category' and 'post_tag '. As you already know WordPress has three built in taxonomies 'category', 'post_tag' and 'link_category'. Further, plugin trace two WordPress post types 'post' (normal posts) and 'page'. When you know this and that, you can easily modify plugin to index your_custom_taxonomy and your custom_post_type.
You need to modify two files: az-index-admin.php and az-index-cache.php. If you don't need to index your posts, the most easiest way to make it work with custom post/taxonomy is to change 'category' into ' your_custom_taxonomy' ($taxonomy), (there is several occurrences in both files) and to change 'post' into 'your_post_type' ($object_type), there is several occurrences in az-index-cache.php. And that's it. Of course, with little extra effort you can add your custom taxonomy (not change 'category') but this is for sure the most easiest way to make it.