In Oedipus, we do have some kind of foreshadowing of the final revelation even before the prophet arrives. Look at the declaration of curses from the King's mouth. It starts to become clear that a revelation is coming.
After Teiresias leaves, Oedipus and Creon get in a major fight regarding the news Creon brings--that the murderer of Laius is living in Thebes and must be removed. In that discussion, the words banish and exile are bandied about by the two of them and even the chorus.
Jocasta actually tells the story of Oedipus and his birth, which of course is a direct foreshadowing of the events which will soon be revealed. Then Oedipus tells his story, adding to the depth of the upcoming revelation.