Yes, because it looks like you made several shortcode directories on the same page, so if the contact argument is in the URL (when you click on message), every one of those shortcodes is going to return a contact form. That’s the way shortcodes work… they are not aware of each other, they just return pure html content back to WordPress.
If that’s the way you are going to set up your directory, using multiple directory shortcodes, then you do need to use a completely separate page for the contact form. Usually that would be your “contact” page, but you already have a contact page set up. So, either you need to use the PTA contact form shortcode on that contact page and have it handle all of your contact needs, or you need to create a second contact page for use just with the directory.
Either way, you will need just the contact form shortcode on its own page, then once you have that set up, select that page for the contact form page option (instead of None), and everything will work fine. Additionally, that contact page will work all by itself and have the list of all your members pre-populated, so they don’t have to go through the member directory first to select a recipient. Unless there is something on that existing contact form page you really need to do differently, I would just replace your existing contact form page form with the shortcode for the pta contact form, and set that to be your contact form page for the directory options.