I honestly get what you're trying to say, it just misses the point. You're focusing on the wrong things, namely, the other people. CHIM isn't about the other people, its about the individual, once you start trying to discuss the 'other people' you miss the point, just like when you start talking about the power associated with it you've missed the point.
Plus you're still starting from a false assumption. Its not just in your head when you achieve CHIM, its not just "YOUR" dream; you take control of THE dream, you're realizing a fundamental truth about the universe. You can say that you make the dream your dream, however this does not create multiple dream realities, timelines, dimensions or anything else - its all still the dream.
When you have control of the dream there are no real 'other' people. The 'other' people
do take part in whatever possibilities the one with CHIM should choose to employ, the fact that they don't know they're participating in it doesn't make any difference. They don't know its a dream but they can still see it and they will see whatever the one with CHIM decides to do, any power that the person with CHIM decides to exercise still occurs within the linear timeline. There is only one linear timeline just like there is only one dream, only one godhead.
However as I said, all this grossly misses the overarching point of CHIM.
Imagine that you yourself realized that everything was fake. That wouldn't mean you knew how to get out of it, it would only mean that you knew you could do anything within it. It would mean further meditation and exploration and so on to be able to find the way out.
The point of CHIM is that it is the way out of it. The realization is the power.