By default projects are created in Public mode. This means that every project you create will be available for every user in the account even for new users.
To make it private you just need to turn the Public mode off and set permissions.
Users set up as coworkers in your account are not allowed to view projects. If you want a coworker to be allowed to collaborate and track time spent on a project, you first need to assign him to the project. You can do so when adding a new project or when editing an existing one.
To view and manage project permissions click on ‘Set Permissions’ and select from the list the users that should have access to the project.
After selecting the required users don’t forget to click on 'Apply' to update the project permissions. Once you've granted project access to a user, he'll see the project on his projects list.