Is expiation obligatory upon one who swore not to masturbate with his hand for a month, then masturbated without using his hand?

Oaths are based on the intention of the swearer. If he intends by his oath something that the word can bear, the oath is directed towards that, whether it conforms to the apparent meaning or contradicts it. What you did is forbidden masturbation, and repentance is obligatory upon you. Expiation is not required of you because your wording "forbidden masturbation" contradicts your intention "masturbation by hand"; for the intention takes precedence, even if it contradicts the apparent meaning of the word.