He does have some understanding on how the grey matters trick and exploit humans, which is to use the victim's memory. In chapter 158 the anomaly used Hama memory, Yagi manage to figure that out, even Yume was suprised.
edit: after re-read again, yeah no clue how their faces is in the manager dream, unless its the flower that saw their faces and inject into her dream to make it as real as possible, because the manager did say the all of the flower would face her, and Hama feels the flower is watching them.
I think that the flower isn't pulling from the manager's memory or anything it saw, but just reality itself. So it figures out the most realistic path for a dream to be achieved.
The owner wanted a flower that could grant wishes, and the price for such a power is life. So the flowers in the dream ate the employees to feed the Dreamin flower. She knew Chacha, and could call her for some advice regarding the strange events—and also as an easy sacrifice, since she said the employees "quit" when they'd been taken by the flowers. The use of the word "quit" instead of "disappeared" or "they just stopped showing up" tells me she was probably aware. Chacha is involved in gray cases enough to recognize what it is and suggest hiring Hama and Yume as part-timers.
It all lines up pretty logically with how things could go in reality if the flower could grant wishes outside of dreams. It's basically showing a potential path/timeline based on if the flower DID have that power outside of dreams. Like a vision of
a future. Think of that multiverse concept where there's an infinite number of worlds that branch off from every decision.
There's just one flaw, which is what REALLY interests me:
The Dreamin flower didn't include Yume's power. In reality, that shop would have stunk to high heaven to her. So, why didn't her powers exist in the dream world? Is it because her powers are based in gray and the flower can't copy other gray things? Or are the dreams more like tapping into glimpses of alternate timelines/universes, and found some alternate universe where Yume doesn't have that power?
We know that other universes exist in this story, and that there's another Hama and Yume in at least one world. So, if the flower DOES show visions of other universes where the wish is granted, is that power unique to THIS Yume?