Prior to issuance of its initial certificate of authority, the health care plan shall appoint the superintendent and his successors as its true and lawful attorney upon whom may be served all lawful process in any action or legal proceedings against it by a resident of New Mexico or where the cause of action arises in this state. In the appointment the health care plan shall agree that any such process so served shall be of the same effect and validity as if served on the health care plan direct. The appointment shall continue in force irrevocably so long as any liability of the health care plan under a subscriber’s contract in this state remains outstanding. Process shall be served upon the superintendent in the same manner and subject to the same conditions as provided in Section 99 [59A-5-32 N.M. Stat. Ann.] of the Insurance Code as for service of process against insurers.