See ASTM C109, section 10.5 . You keep the specimens in the moist room for 20 to 72 hours. If removed from moulds before 24 hours, keep in moist room until 24 hours then immerse in lime saturated water. Strange wording - the water storage tanks seems only to apply to the cubes removed from mould before 24 hours (editing problem?).
Section 10.6 says to test the specimens right away after removal from moist room/moist closet for 24 hr test or from storage water in other cases.