What you are describing is a "hidden variable theory", but it has been shown (See "Bell's Theorem") such a theory cannot be true. QM is stranger than that.
To be clear, what really happened under MWI is that the wavefunction "branched" into two around the time you created the two particles, and the two branches spearated from each other in configuration space just as the two marbles in your analogy separated in physical space. When you did the measurement, you merely realized which branch you are in.
Where the analogy fails is that the probabilities in QM are inconsistent with there actually having been some hidden choice of marbles made beforehand.