The way I expect your demux to work is like this. 4 address lines indicate which relay is to be switched. A data line indicates if the selected relay is to be switched on or off. An enable or latch line indicates that the 4 address lines and the data line are ready to be read by the Arduino. This enable/latch line might indicate this by being high, or by being low, or by changing from low to high or from high to low, any of those would work. But without a latch or enable line, you would get unwanted switching of your relays when you did not intend them to switch.