Nowadays many jobs are outsourced. Some agencies take the work being outsourced and employ people themselves to do such outsourced work. In such a case, the employee of the outsourced agency has no connection with the original whose work he is doing.
Similarly, in your case, you are writing that you are working with a contractor, who may be handling the work outsourced by PSU and for doing such work hired you. Please verify who gave you appointment letter (if at it is given). If the Contractor has given the appointment letter , you are the employee of the Contractor and not that of the PSU.