I’m answering this as though the layer where Cobb assembles his team is “reality” for them. I know that there are theories that this isn’t ultimately true, but for the purposes of discussion, let’s assume that it is.
First, there’s a cool mock-up of the machine here:
Depending on the size of your screen, you have to scroll over to find the arrow to navigate through the pages.
The mock-ups seem to confirm the impression I got from the movie, which is that the device’s only function seems to be to regulate the correct dosage of the drugs that put the subject under. There’s nothing that feeds information back from the dreamers to the PASIV device.
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.
With all of this in mind, the answer is that the device in the dream doesn’t “work” in the same way as the one above…but its effects are the same due to the shared reality.
The PASIV device we see in the dream isn’t a real device, but a double of the device made by the dreamer who creates the “level.” However, the minds of all the dreamers are still following the same set of rules and all “go under” as though they experienced another dose of the drug in this dream-world. The dream-within-a-dream is therefore still a part of the dream-world in the level above it, but they go “a level deeper.”
The way to think about it might be to examine the physical reality of the dreamers. They’re going deeper and deeper into the levels of the dream, but in “reality” they’re all still asleep on the plane. Once you get past that first dose, everything happens in the mind.
Remember, the PASIV device administers a drug. Once someone has experienced the drug once, they’d be able to recreate its effects for their dream selves. There’s evidence of this phenomenon in the real world. One of the most famous descriptions of this comes from Terrence McKenna in his talk “Alien Dreamtime.”
“I remember the very, very first time that I smoked DMT. It was sort of a benchmark you might say, and I remember that this friend of mine that always got there first visited me with this little glass pipe and this stuff which looked like orange mothballs…”
He describes a bunch of crazy experiences and then later says:
“And one of the things that I learned about DMT was that if you’ve ever had it, even just once, then you can have a dream, and in this dream somebody will pull out a little glass pipe, and then it will happen! It will happen just like the real thing.”
Basically, using the terms you can find in the “Dreams” link in the upper right corner of this page, the PASIV device is a DOUBLE TRIGGER that induces SINK.