jklyn on "How to show multiple CPT by category in custom archive page?"

Can anyone please tell me how can I show multiple CPT by category in archive page. Lets say I have CPT “product” and another CPT “news”. I managed to get the CPT product to list on my archive page but I can't list news page. I renamed archive-news.php. I tried this code to list my both product and news but it only shows my product page which is on my archive page. It doesn't show archive-news.php.

//add multi custom post type to tags and categories
function add_custom_types_to_tax( $query ) {
// Return right away if in admin or not working on the main frontend query
if ( is_admin() || ! $query->is_main_query() ) {
return;
}

// Check if we're on a category or tag archive. If so, add our post type
if( ( $query->is_category() || $query->is_tag() ) ) {
// Get all your post types
$post_types = array('post' , 'product' , 'news');
$query->set( 'post_type', $post_types );
}
}
add_action( 'pre_get_posts', 'add_custom_types_to_tax' );

My archive page code is:

<?php
if ( have_posts() ) :
the_archive_title( '', false );
the_archive_description( '<div class="taxonomy-description">', '</div>' );

while ( have_posts() ) : the_post(); ?>

<h3><?php the_title(); ?> </h3>

<?php endwhile;

the_posts_pagination( array(
'prev_text' => __( '<<', 'twentysixteen' ),
'next_text' => __( '>>', 'twentysixteen' ),
'before_page_number' => '<span class="meta-nav screen-reader-text">' . __( '', 'twentysixteen' ) . ' </span>',
) );

else :
get_template_part( 'template-parts/content', 'none' );

endif;
?>