If an Eastern Rite Catholic marries in the Western rite, does he/she need to formally change rites?

All the Eastern rites of the church are in communion with the Pope, else they would be a variant of Orthodox Christianity. However, say there was an Eastern Rite man marrying a Western Rite woman. If they were to have a ceremony in the Eastern Rite, then a Western Rite priest could not preside, and the woman would have to change Rites. This is a fact I know from my Priest who asked a Canon lawyer familiar with the Melkite and Western Canon's. Is the reverse true? That is, if the couple wants to marry in the Western Rite, will the Eastern Rite man have to formally change rites to the Western rite?