The 'Add Time Off' button on timesheet is used to submit the unplanned time off taken by the employees. (For example, sick time). Since the time off day is in the past, it can be directly entered by employees on timesheet, than booking it.
If your organization wants employees to only book their time off, and not to allow them to add it on their timesheet without approval, then please follow the instructions to configure.

1. Log into 'Web TimeSheet' with administrative rights.
2. Click on the 'Administration' icon at the top.
3. Select 'Permissions', from the left side pane, under the "Users/Departments" category.
4. Click on 'Edit' button, next to the permission name or click on the user's (assigned) permission from where the "Add Time Off" button has to be removed.
5. Expand 'Timesheet' option (by clicking on the '+' symbol next to it).
6. Uncheck the option "Enter time against time off types not requiring booking"
7. Click on 'Save' button at the bottom of the current page.