I am using PayPal buttons for the six different membership levels I have set up. When signing up the user clicks on the PayPal checkout button and is taken to PayPal. Once they pay they are returned to the website to a page that tells the user to check their email for more information, but there is no place on the return page for them to add their information, no email is sent to the new user and a new user is never added to the database.
When the visitor completes the payment with the PayPal button, that doesn’t automatically create the user account in WordPress. He has to signup on your site an account at /wp-login.php?action=register.
He should be getting an email, though. Does that happen with every single user or only some didn’t get it? Please see: https://s2member.com/kb-article/troubleshooting-email-delivery-problems/
I hope that helps.