he basis of SSO is essentially that your customers only have to sign in at one location. Generally this would be your website. We would redirect registration requests to your website, and login clicks to your website, should they want to log in from the community side of things. So that once they are logged in, they are logged into everything. Giving your customers a unified experience.
Any specific requirements such as group changing for access, as you mention above, you would discuss those requirements with our sales team. Bear in mind, the key here is "Custom". So nobody can really tell you exactly how yours works, as by definition its custom.