Who is a project supervisor
A project supervisor is a person with rights to edit a project.
Where do I define project supervisors
Project supervisors are defined in the very last step of creating a new project (Summary).

When the project has already been created and you need to add a new supervisor, just click the Edit project button and use the bottommost field to add more people.

Who can become a supervisor
Anyone with a Manager or Admin role (including the Owner) can become a supervisor. Employee role users cannot become supervisors, as they cannot access project budgets – the only thing they can do is track time.