Custom taxonomy term links out of order

Use wp_list_categories() instead, which handles the display and ordering of hierarchical terms.

Despite its name suggesting that it’s just for categories, it works with custom taxonomies too:

$taxonomy_args = array( 
    'public'   => true,
    '_builtin' => false,
); 
$output="names";
$operator="and";
$taxonomies = get_taxonomies( $taxonomy_args, $output, $operator ); 

if ( $taxonomies ) {
    foreach ( $taxonomies as $taxonomy ) {
        echo '<ul>';

        wp_list_categories( array (
            'order'    => 'ASC',
            'orderby'  => 'name',
            'title_li' => '',
            'taxonomy' => $taxonomy,
            'show_option_none' => '',
        ) );

        echo '</ul>';
    }
}