It seems like you are asking for the working method of PASIV. I am afraid it has never been explained how does the whole dream sharing works. Even not in the demo they provided i.e. in http://www.pasivdevice.org/ I went through all the pages. But it merely shows how the injection of the sedatives is done and the physical outfit of the PASIV machine and procedure of dream sharing, but not the working method of the machine. In my opinion, it would never be known because in reality this type of machine does not exist. So revealing any unscientific explanation is mostly unexpected. I support this theory:
Therefore the dream sharing they experience must be in some way a psychic phenomenon facilitated by the drug and/or training. This doesn’t get explored much in the movie. The mechanics are pretty much glossed over.
At the end I can only add:
The PASIV is a concept that can potentially inspire researchers and inventors to produce real-world technology that lives up to the fiction, literally opening up possibilities limited only by our imagination.