When your WooCommerce affiliate users sign up using the sign up widget, they will just be providing an email address. Upon doing so, they will receive a welcome email with their referral link and a button to complete their registration. When they click on the "Complete Registration" button they will be taken to their WooCommerce affiliate user area where they set their password and login. By default users will be able to update their profile info at anytime, however if you would like to force them to complete  the profile fields right away, you should do the following:

1. Go to Admin -> Setup

2. On the settings page, check the box that says "Require All Profile Information After User Logs In", then click update.