The Observer role is a special role that's available under the Starter, Pro and Enterprise Plans only and has only limited permissions.
When you invite Observers to a certain project, they can also see all your projects and all other recordings under the "All Recordings" tab.
If you want your Observer to see only sessions from a specific project and no other project, you'd have to make all your projects 'Private Projects' and make sure the specific Observer has been added to the required Private Project as well.
We recommend you do this, especially when you invite an external stakeholder such as a client to be an Observer.
The Private Project feature is available under the 'Pro' and 'Enterprise' Plans.