At Disneyland in the adventureland Bizarre, there used to be an animatronic shrunken head that would tell your fortune.
Also in the same area, there was and alcove with a "magic lamp", a genie, would appear in a cloud of smoke and tell you your fortune.
Back when the Tiki Room opened. There was an animatronic Parrot that sat at the entrance to the Adventureland, calling people to "come see the tiki room" It caused such a traffic jam, it was moved inside the Tiki garden pre show, and eventually removed all together.
I don't know if these are what you are referring to. But they sound similar.