I mean, I get that time is a little different in that you will eventually experience and remember all possible solutions as you stand there watching the system, because classical time is a linear chain of events. In the multi-world case, it's a branching chain, and your experience and memories of the different solutions are stuck in their own branches.
That does make worlds weird and different from the other dimensions, but we accepted time as being weird and different from space for a very long time.
> Now, if we try an experiment where the interaction at time T1 happens with a particle, and you have detectors at positions X1, X2, Y1, Y2, you will find it with equal probabilities at any of the 4 locations. However, if at X and Y there is a detector, and you detect the particle at X, it will never be found at positions Y1 or Y2. You have to update the Schrodinger equation after you find out that the particle is found at X, which is never how classical mechanics work.
This makes total sense if it's actually a wave and the particle is merely a solution for a particular world W. The detector didn't change anything about the wave. It just coupled you to the wave system earlier, so now your branch of the many-world tree can only see the subset of solutions that correspond with whatever you detected. The only thing that has changed, though, is your ability to see the other solutions. You branched earlier, so now each branch you exist in only sees a subset of the full solution.
That said, I am not a physicist. The many worlds explanation was just the first thing that actually made sense to me about quantum mechanics. It's so conceptually simple.