No. There is not a one to one relationship with clients and projects like some other software. With Intervals a non administrator can see any projects where they have been specified as a member of the project team regardless of which client they are associated with. If a person does not have access to a project they do not know it exits.
When a person is associated with a client there are some convenience features that will show the projects for that client first in the list when editing the person’s project permissions (screenshot below), but they can be assigned to any project, despite their association with a client.
If you are unfamiliar with the hierarchy of elements within Intervals, we recommend checking out the project hiearchy help page. It can help clarify the relationship between clients, projects, modules, milestones and tasks.