When this chapter becomes effective, all persons then holding positions not included among those exempted by the city Charter shall have a permanent status if:
(A) They were employed in positions on the date of passage of this chapter (May 14, 1968) and have served their full probationary period.
(B) They shall serve a probationary period of one year or any other period as may be prescribed by this chapter for the position held. ('70 Code, § 153.02)