I had always thought that they came into existance through the power of Lavos. After all, Lavos can affect time, and has the power to make dreams come true, as all the Zealians said.
It's possible that the creators of the Mammon Machine (Melchior, Belthasar and Gaspar) would at least have been close to the flame or Lavos' energy for a longer period of time than anyone else, and the energy might have gotten into them and created their dreams.
Also, I wonder if anyone besides Melchior and Crono and co can see Masa, Mune and Doreen. I kind of thought that they only show themselves to certain people, or atleast to the Heros of Time.
