Have you confirmed whether the counter value in the database is being incremented? I don't mean to tell you something you might already know, but check the wp_options table, and search by option_name for cf7-counter.
If the value is being incremented, that means you've set up the action correctly. Then from the tutorial, it looks as though a shortcode is being used to output the count. If the shortcode tag is included in the main content field of your post/page, it should be applied automatically by the filter, the_content.
If however you want to render it in the header of your site, you'll probably have to use:
echo do_shortcode('[CF7_counter]');
R.