I’ve never used is_page_template() but I have had good luck with is_page('new_search') regardless of which conditional you use some things to check.
Is the is_page_template('new-index.php') working. you may test this by doing something like:
if ( is_page_template('new-index.php')) { wp_die('new search page');}
You should also use wp_register_style and wp_enqueue_style in your functions.php hooking in the the wp_head which you should have better luck with.