They have to be replaced with the new domain url.
Usually scripts and styles are loaded with
wp_enqueue_style in the theme's
functions.php. That's the most common scenario.
This function takes an
$src parameter which is the absolute URL to the resource, and the best practice is to use
get_stylesheet_directory_uri to retrieve the URL to the folder containing the script. This way, if the site is moved, the URL will change with it.
It might be that those were hardcoded strings. That's why they're still the old ones.
Scripts and styles loaded from a plugin should use
plugins_url in the $src parameter.
wp_enqueue_style( 'prm_style', plugins_url('/assets/style.css', __FILE__ ) );