Custom Taxonomy Not Showing in Front-End When Outputting a Custom Post Type with WP_Query()

From your explanation above I understood that you want to show custom taxonomy you have registered for that post type.

the_category(); fetches the default category that comes with the default post.

For rendering custom taxonomy you need to add something like this:

$terms = get_the_terms( $post->ID , 'your custom taxonomy slug' );
foreach ( $terms as $term ) {
 echo $term->name;
}