After the completion of the probationary period, the employee’s seniority shall date from the day of original employment. Employees seniority shall be by institution or campus at which he is employed, unless a lesser unit shall be determined by the Merit Board in an agreement with the employees involved. Whenever it is necessary to reduce the number of employees those with the least seniority shall first be laid off, and their names placed on a reemployment register which shall take precedence over any other register. Reemployment shall be made in the order required to preserve the seniority rights.