This is the typical payment/registration process with WishList Member:
a) Person clicks Payment Processor button to purchase the Membership Level
b) Person pays through Payment Processor Site
c) Person is redirected to a page on the WishList site where they can select their username and password
d) Person is automatically logged into the WishList site
e) Email is sent to member with their username and password
So from the user’s experience, they pay at the Payment Processor site and then they select their username and password as they are automatically redirected and logged in to your site.
That being said, the latest versions of WishList Member (2.8 and higher) include an integration with Stripe and WishList Member 2.9 includes an integration with PayPal Pro. These integrations allows the person registering to stay on your site when they pay. This is due to how Stripe and PayPal Pro function.