Notwithstanding section 5121.04 of the Revised Code and except as provided in section 5123.194 of the Revised Code, the liable relative of a person with a developmental disability who is a minor receiving residential services pursuant to a contract entered into with the department of developmental disabilities under section 5123.18 of the Revised Code shall be charged for the minor’s support the percentage of a base support rate determined in accordance with division (B)(2) of section 5121.04 of the Revised Code.