Hello Lalith
Watched projects are user specific. Each user maintains their own list of watched projects. Users add projects to their watched projects for the purpose of creating a navigational shortcut. This decision usually depends on how often a user needs to visit the project and will vary from user to user. A user does not need to be a team member of a project to add a project to their watched projects. As stated above users cannot add projects to other users watched project lists.
Visibility of a project is not managed by watched projects. Project visibility is managed by permissions, project access control and project teams. If a user is a member of the project then they should be added to the project team. Notification settings can be set to send a notification to a user when they are added to a project team.
Cheers
Ken
