Payment shall be made in accordance with the terms of a final apportionment, to a school district for expenditures, or commitments therefor, which have been made by the district subsequent to the date of the proclamation of the Governor proclaiming a state project in the area including the district, for any items approved by the board in the apportionment. However, if expenditures were made for, or work was commenced with respect to, any item so approved, prior to the time the application of the district containing the item was received by the board, payment or reimbursement for the item shall be made only upon authorization of the board by special resolution citing this section.