Drain line adapter recommendation for reverse osmosis kit + dishwasher?
That short piece of black rubber hose (with 2 hose clamps) that is included with the adapter in your link should attach directly to the copper pipe. Then you clamp your dishwasher hose to the proper size barbed tube; the RO drain uses the quick disconnect.

If the black hose is too big, use an adapter:



You should know that your dishwasher drain should be equipped with an air gap, or at least put an anti-siphon loop in there:



diagram stolen shamelessly from the web