I noticed that Auto Tweet is posting all new posts to Twitter, including custom post types that are not public. Is there a way you could offer an update or patch that fixes this.
Since WordPress 3.0 registering your own custom post types has been a feature. When you register these post types you may declare them public or private. Now if the post type is declared public, I would totally understand posting a tweet when you create a new custom post. But if the post type is declared private, I feel that there should be no tweet posted, as there is no public facing page for that post.
Please check out the sitemap.xml generation part of Yoast SEO plugin, there you may configure which post types are added to the site map. Maybe you could implement something like that in your plugin's options panel.