The original use of "Roma locuta, causa finita" is attributed to Augustine, who opposed Pelagianism.  Pelagianism was condemned at the Council of Diospolis in 415 and a synod in Carthage in 417. Pope Innocent I condemned Pelagius and his doctrine.

Augustine's Sermon 131 says "Two synods have written to the Apostolic See about this matter; the replies have come back; the question is settled; would that their error be similarly settled." 

But it was not settled. Innocent had died in March 417 and the new pope, Zosimus, reopened the case, and made noises favorable to Pelagius. Eventually the emperor Honorius condemned Pelagius, and Zosimus followed the emperor's lead in condemning Pelagius in the summer of 418. Then Zosimus died that autumn, and Pelagius tried to get the case reopened.  Augustine used lay contacts (and a hefty bribe) at the imperial court to come down against Pelagius.

Thus, Rome spoke several times, saying different things, and the case remained open for some time.