From the term “Extraction” I suppose that you are talking from the extraction your products out of an aqueous reaction solution/suspension with DCM.
That your “postulate” holds in this case you must take care, that the pH of the aqueous phase is all times lower then pH 6 - 7, because Eugenol is a Phenol and acts there wile as a weak till medium Acid. Holding the pH such low prefers the UN-dissociated side of the acid balance/equation much more.
In this “acid” state the Eugenol is quite UN-polar as also the Acetate is.
Because water is a very polar solvent and DCM is contrary a quite UN-polar solvent, your products like the DCM very much more then the water.
That does conform to the thumb-rule: “The same likes similar”.