The state shall reimburse each county for the cost of care of any child placed under the custody of a county department pursuant to Section 8805 or 8918 of the Family Code. County claims for reimbursement of expenses incurred pursuant to Section 8805 or 8918 of the Family Code shall be filed with the department at the time and in the manner specified by the department, and the claims shall be subject to audit by the department. Whenever a claim covering a prior fiscal year is found to have been in error, adjustment may be made on a current claim without the necessity of applying adjustment to the appropriation for the prior fiscal year.