Whenever tide and submerged lands granted in trust to a county by the Legislature are included within a city’s boundaries as the result of that city’s incorporation, trust title to such lands shall pass to such city only upon specific authorization and direction of the Legislature and at that time all papers, records, and all other documents pertaining to such lands and the administration thereof shall automatically become the property of the city and shall be transferred to the possession of the appropriate city officials by the county officials having possession thereof; provided, that the city shall pay to the county all costs necessarily incurred in making such transfer.