The Masters of the Great White Lodge are borrowed from Theosophy, relocated to Sirius, and given a Templar chain of command. They spoke through Di Mambro, appeared in the sanctuary, and issued instructions that outranked anyone present. The appearances were staged with hardware, and this is not a hostile inference — the equipment was found, and its installer was a member who left and was later murdered. What that means for the members is the uncomfortable part: a person could have a genuine, life-reordering experience of contact with a Master, in a room, produced by a projector.