The Box Files tab seen on all records is created by the User Event Script 'Box Files Tab' from Bundle 28044 (Box Files - New!)
To remove the said tab from other users' or employees' view, proceed with the following steps:
1) Navigate to Customization > Scripting > Scripts
2) Look for the 'Box Files Tab' User Event Script. Click the 'View' link next to it
3) Under the 'Deployments' tab, click on '-All Records-'. Click on Edit
*note that the 'Applies To' column might change depending on whether you edited the script deployment. By default, the Box Files Bundle installation sets it to '- All Records -'. For more information on editing Script Deployments, please see the Define Script Deployment article.
4) You should now be in the Script Deployment Screen for the 'Box Files Tab' script
5) Under the Audience tab, select the desired Roles, Departments, Groups, Employees and Partners that will be able to access the 'Box Files' tab. Save the Deployment.
Note: For more information on modifying the script deployment audience, please refer to Defining Script Audience