Create a Reporting Manager ID by following the instructions here.
To add the reporting Manager to the TimeTracker users,
- Go to the TT Users tab
 - Add the "Reporting Manager" name while creating the TimeTracker users, OR
 - From the TT User edit page, go to the Reporting Manager" field,
 - Search for the Manager's name, (to whom the user reports)
 - Click the save button.
 
By adding the Reporting Manager to the user
- The Manager can see the time details and approve them.
 - Assign Projects to the user
 - Assign Tasks from the Project Management module,
 

Note: Even the Reporting Manager should be created as TT User in Salesforce, only then you can add them as a Reporting Manager to the user.