no you don't need the email role.
could be several causes though..
spf / dkim / dmarc
invalid helo name
no / mismatched ptr records (both ip4 and ip6)
phpmail is most likely submitting mail to a local postfix instance without any problems so there's not going to be any php errors to log.
check /var/log/mail.log or /var/log/postfix.log
both on the local instance and the smart host.
