Doesn't this system have more privacy constraints? E.g. the website you're visiting shouldn't be able to learn anything about your identity beyond the attribute

Doesn't this system have more privacy constraints? E.g. the website you're visiting shouldn't be able to learn anything about your identity beyond the attribute (above 18), and the identity provider shouldn't know anything about which website you're visiting. It does seem like people tried very hard to make it privacy preserving.