... And so the Master developed the multiple personalities. If you played all the way to the end of Fallout 1 and actually had a conversation with the Master (DEATH BY WORDS), you might remember that he would often talk in different voices.
Whose to say that the Master that you killed was the ACTUAL master and not just an extension of the master, who is comprised of both technical and organic material. Theoretically he could have absorbed a modem into a centaur and remote controlled the Master that you talked to.