Summary:
A new user is promoted recently and is assigned as supervisor to a group of users in Web TimeSheet. The supervisor has supervisor and project leader permissions assigned. The supervisor runs a time based report in-order to report only on all of the direct reports time data but the supervisor is able to see only the supervisor's own time data and not the direct reports data.
This behavior is found only for one specific supervisor and there are other supervisors (with identical permissions) who are able to report on their direct reports time data using one of the time based reports in Web TimeSheet.

Cause:
The supervisor security filter on the report will only return data for those timesheets that the user is a supervisor for. In the case of the other supervisors who are able to report on their direct reports, have been supervisors on every one of their direct reports timesheets, for a long time, while the affected supervisor appears to be a new supervisor.

Resolution:
Open timesheet and future timesheets would have the current supervisor associated to the direct reports timesheets and supervisors will be able to report only the direct reports, current and future timesheets and not past approved timesheets. Backdating the effective date of the supervisor, under the user profile does not mean that the new supervisor can report on the direct reports past time data; this does not affect the past approved timesheets because those will have the previous supervisor's name associated to it and will remain that way until the timesheet is reopened, edited and saved again.

Note:
Supervisor should be able to report on their direct reports, without needing to be in the approval path.