After the effective date of the boundary change, the officers of the affected counties shall complete all proceedings necessary for the assessment or collection of state and local taxes for the current year with respect to the affected territory. Subject to Section 23213, all actions taken by the officers of the affected county before the effective date of the boundary change shall be deemed performed by the officers of the county in which the affected territory is situated after the effective date of the boundary change, for the benefit of that county.