As you have developed on Windows and not Linux it's most likely a case-sensitive matter. Your files/folder may be named Auth/Auth.tpl but you can on Windows load them as auth/auth.tpl. But you should load them as Auth/Auth.tpl. So you need to check your capitalization.
You should also move your files one path down. You should not access CI as /public/, so your index.php are placed in the wrong folder.