Will Postman allow auto-reply from SMTP?

I was hoping Postman would allow my Dreamhost email to trigger an auto-reply to the sender. If someone contacts us through this generic WP contact form, no auto-reply is sent. I assume that’s because the email is actually sent from WP, not the sender (even though when it gets to me, I can reply to the sender).

Am I misunderstanding what Postman does? Will Postman make the email from our generic WP contact form to be sent directly through our Dreamhost mail server (thus activating the auto-reply from Dreamhost)?

I’ve been banging my head against this for hours. I can’t seem to find a simple auto-reply plugin that will work with the WP contact form. Perhaps I need a different contact form plugin (with a built-in auto-reply option)?

The page I need help with: [log in to see the link]