Bob is a scientist, they have hooked a computer to the R vs T experiment and when R occurs the screen flashes red. When the screen flashes red, red photons collide with Bob’s skin and eyes, signals enter their brain and they observe a red screen, and they remember it. So, given the state of redbob, I think it’s reasonable to say that perceived R.
These are all classical assumptions which Many Worlds denies. Again, you keep repeating classical descriptions to explain Many Worlds. I do not know how I can explain it as I’ve already went over this several times. You do not get discrete events out of the Schrodinger equation, there is no “redbob,” there is no photons colliding with Bob’s skin and eyes. None of this happens if all you have is the Schrodinger equation.
I don’t think it works the other way either, I don’t see why anything in quantum mechanics specifically would give any more credence to determinism than classical mechanics which is also deterministic.