After you joined the network as a normal client membership, now you need to redirect to the affiliation program page to join it, the page URL is as follows:

https://portals.aliexpress.com...

As you enter this page you will think that you need to have another registration submission.. but no, you don't. All what's required is to have a client membership to login or sign in. But note that you need to confirm your account by following the confirmation link on your registration Email.