Taxonomy Page

I got a custom taxonomy called author and I’m trying to create a page for it. This is what I’ve done so far:

1. I registered the taxonomy

add_action( 'init', 'register_taxonomy_author' );

function register_taxonomy_author() {
    register_taxonomy(  'author', 'post',   //Let WordPress know that the artist taxonomy has posts
        array(
            'hierarchical' => false,
            'label' => 'Authors', // This tells WordPress how to label the various user interface outlets for the artist taxonomy
            'query_var' => true,
            'rewrite' => array( 'slug' => 'author', 'with_front' => false ))
            );
}

2. I created a new template called taxonomy-author.php and pasted the code from my category page there.

Then I clicked the permalink settings to refresh it. Then I went to Posts > Authors > View which directed me to mysite.com/author/term/. So far so good. However, this page uses the index.php instead of taxonomy-author.php and displays all posts. What’s the problem?