You’re using get_the_author_meta
If you used get field it would need to be
<?php
$user_id = 'user_'.$user->ID;
$publisher_photo = get_field('author_header', $user_id);
$image_src = wp_get_attachment_image_src($publisher_photo);
echo '<img src="'. $image_src[0] .'" />';
?>
