“In Buddhism, a tulpa is a spiritual double. This entity looks and sounds exactly like you. You can control it, or it can control you. It can act independently of you.” Is this phenomenon real, and described accurately, and can you explain its origin and its consequences?

The idea of the tulpa, as you saw intuitively, is the perception there is a higher self, that people have more than one component in their makeup. So this is a kind of advanced teaching based on those quite adept with intuitive reach, who are able to channel the higher self and see this as a separate entity and know it to be a universal phenomenon even though most individuals cannot get a sense of its presence. So this is a parallel with your teachings, to some extent, but not matching the description given by Buddhists who have added some additional descriptive flourishes here in an attempt to come to grips with its meaning. These are not especially useful or accurate because they do not convey much about useful properties and the importance of the phenomenon.