Any state office, commission, department or institution may also pay the moving expenses of a new employee, necessitated by his or her acceptance of state employment, pursuant to mutual agreement with such employee in advance of his or her employment. Payment for all expenses authorized by RCW
43.03.060,
43.03.110 through
43.03.210 including moving expenses of new employees, exempt or classified, and others, shall be subject to reasonable rules adopted by the director of financial management, including regulations defining allowable moving costs: PROVIDED, That, if the new employee terminates or causes termination of his or her employment with the state within one year of the date of employment, the state shall be entitled to reimbursement for the moving costs which have been paid and may withhold such sum as necessary therefor from any amounts due the employee.