The fee, provided for by the provisions of section 2-3408, shall be deducted, as provided by sections 2-3401 to 2-3416, whether such poultry and eggs are stored in this state or any other state. Any fees remitted to the director may be refunded by the director upon the written application of any producer for a refund of the amount deducted by the first purchaser. The application for refund shall be submitted to the director within sixty days from the date of assessment of fees and shall have attached thereto proof of the fee deduction claim by the applicant.