What ever you do is going to end up within the h1 tag, but this will keep it out of the menu etc.

function personnel_filter($x)
{
    $value = get_field('position');
    $x = '<div class="person-sub">' . $value . '</div><!--person-sub-->' . $x;
    return $x;
}

function jma_person_title_cond($query)
{
    global $wp_query;
    if ($query === $wp_query) {
        add_filter('the_title', 'personnel_filter', 10, 2);
    } else {
        remove_filter('the_title', 'personnel_filter', 10, 2);
    }
}
function jma_child_redirect()
{
    if (is_singular('personnel') && get_field('position')) {
        add_action('loop_start', 'jma_person_title_cond');
    }
}
add_action('template_redirect', 'jma_child_redirect');