After a user accepts your invitation, he will be added to your Universe's user list. At this stage, the user doesn't belong to any of the user groups and doesn't have the permissions necessary to view projects and tasks in your Universe. A Universe Administrator has to give the necessary permissions to the new user.
You can add him to a currently existing user group, or give access only to certain tasks if necessary.
When the permissions are granted, the corresponding tasks will be shown to the user in the Navigator.