Global asymptotic dynamics of a typical cubic-autocatalytioc reaction-diffusion system, the reversible Gray-Scott system, are investigated. The existence and upper semicontinuity (robustness) in the $H^1$ product space of the global attractors for the family of solution semiflows with respect to the reverse reaction rates as they converge to zero are proved through the approach of transformative decomposition to overcome the hurdle of perturbed singularity between the reversible and non-reversible systems by showing the uniform dissipation, the uniformly bounded evolution of the union of global attractors, and the uniform convergence of the bundle of reversible and non-reversible semiflows.