Pass custom value to custom taxonomy

have you tried building your tag array into a variable and passing that as a parameter to set_post_terms?

 function add_author_taxonomy( $post_id ) {
     global $wpdb;
     if(!wp_is_post_revision($post_ID)) {
         $my_tags = get_post_meta($post_id, 'user_submit_customauthor', true); 
         wp_set_post_terms( $post_id, $my_tags, 'author', true ); 
         }
     }
     add_action('publish_page', 'add_author_taxonomy');
     add_action('publish_post', 'add_author_taxonomy')

;