Actually 'Divo Tito' is dative, 'Divi Vespasiani' is genitive. The 'f' is an abbreviation of filius, son. Divus does mean divine, most emperors were deified after their death (never before).
So the sentence means "The people and Senate of Rome, to deified Titus Vespasian Augustus, son of deified Vespasian".
From this you can infer that the arch was dedicated after Titus' death.