Yes, that’s true. Bifurcation (or multifurcation) should occur to the many world hypothesis every time that entropy increases. In the example of the thrown die the result is a selection of one out of six possible outcomes. That is irreversible. Irreversible actions increase entropy. The die and the thrower multifurcate into six different versions in six different worlds after the result is clear.
In the context of simulations of world it’s conceptually easier to just assume that worlds are deterministic. This avoids such complications as bifurcation happening both through quantum world branching and interventions of simulators. But of course, both happen assuming that the many world theory is true and that we live in a simulation.