Privacy changes when adding new users to a project

I currently have the free version and I’ve created a project on which I want to invite three of my teammates to collaborate. It says my project will no longer be private. Does this mean that my project is searchable within Asana, or accessible from a search engine? When I invite my teammates, does that automatically make my project public? I guess I don’t understand what changes when I add people to my project in the free version. I want to collaborate on the project privately and securely. Thank you!