The county treasurer shall be discharged from responsibility for all moneys deposited by him pursuant to the terms of this Division, with any depository or depositories who may be named and shall qualify in accordance with the terms thereof: Provided, that nothing in this Division contained shall be construed in any manner to change or affect the liability of treasurers having depositories under and in accordance with the terms of this Division, except that such treasurers shall be discharged from liability for moneys so deposited by them in such depositories while such moneys so deposited are in the custody of any such depository.