No, that's not how burden of proof would apply in this instance. Parallel worlds are assumed to have similar cosmologies until proven otherwise.
Under MWI and similar concepts of splitting timelines, branched space-times are expected to have the same cosmological construction. Quantum properties like energy, angular momentum, and electrical charge are conserved as space-times split off. Each branch follows a distinct trajectory in how quantum states evolve, but they retain a history of the past quantum states leading up to the branching event in question. When a quantum event forces timelines to split, the history of each branch is not expected to change retroactively. Each branch follows a coherent sequence of events that includes the states of quantum systems leading up to the branching event. This conservation of history is an essential aspect of MWI that maintains the integrity of each branch as it evolves independently.
Some things have to be proven, other things are assumed true until disproven. All known theories of splitting timelines would suggest a shared cosmological makeup between parallel worlds, the burden of proof actually lies on the opposition to explain the reason for alternate timelines in Dragon Ball
not having a shared spatial makeup.