This depends on the actual couplers you are referencing. Check these links to the
"D" and
"S" couplers. You will notice that the only difference is that the probe and probe seal are different.
If you do have these couplers, you do not require a washer between the one way valve and the tailpiece. If you notice, the tailpiece is designed specifically for this valve. This allows for a seal and holding the valve in place.
If you do not have this coupler, check out the MM Equipment Store for your specific coupler and pull up the replacement parts menu. This will indicate if your coupler requires the seal.