The provisions of this Charter shall become effective January 1, 1960, except that all officials elected at the election held on November 3, 1959, including the President of Council, shall complete their respective terms; provided, however, that, following the expiration of the term of the Treasurer elected at the November 3, 1959 election, the Auditor elected at such election shall, until the expiration of his term, perform the duties and functions assigned to a treasurer of a city under the general law of the State of Ohio and to the Director of Finance under the provisions of this Charter.