This is intentional, because of the various ways themes add an H1 to the front page–some change the site title to an H1, for example; some assume the title will be added as part of the page content (the newer versions of the Sample theme go this route). If you want to use the plugin to output the H1 on the front page the same as it does on the rest of the site, you’ll want to add this filter to your theme’s functions.php file or wherever you add similar code:
add_filter( 'display_featured_image_genesis_excerpt_show_front_page_title', '__return_true' );
That should be all you need, if the banner image is displayed on your site’s front page. Please practice safe coding and make sure your files are backed up before editing PHP.