You do not have to invite Company Admins to every project within a Company. A Company Admin will appear on a project's Crew List once they click into a project for the first time.
A Company may have dozens of Company Admins, and dozens of projects, but not every Admin is managing every project. To ensure only the Company Admins that are working on a project are included on the Crew List (and prevent extraneous names from appearing on a project's Crew List), TiM only adds a Company Admin to a project's Crew List once the Company Admin has interacted with that project.
Company Admins can access new projects via the Company Account drop down menu at the top of the screen.
If you have further questions, please contact: firstname.lastname@example.org