Spatial heterogeneity is a fundamental feature of ecosystems, and ecologists have identified it as a factor promoting the stability of population dynamics. In particular, differences in interaction strengths and resource supply between patches generates an asymmetry of biomass turnover with a fast and a slow patch. The coupling of these two energy channels by mobile predators has been identified to increase stability at different scales by promoting the asynchrony of population dynamics between each patch. Here, we demonstrate that asymmetry has a contrasting effect on the stability of metacommunities receiving localised perturbations. We built a model of an asymmetric metacommunity with two patches linked by the dispersal of predators and in which prey receive stochastic perturbations only in one patch. Perturbing prey in the fast patch synchronises the dynamics of prey biomass between the two patches and destabilises predator dynamics by increasing their temporal variability. Conversely, perturbing prey in the slow patch decreases the synchrony of their dynamics and stabilises predator dynamics. This discrepancy between the responses is due to the asymmetric transmission of perturbations caused by the different distributions of biomass between the fast and the slow patch. Consequently, the fast patch drives the dynamics of the metacommunity and imposes synchrony while the slow patch does not. Therefore, local perturbations can have opposite consequences at the regional scale depending on the characteristics of the perturbed patch. Our results have strong implications for conservation ecology and suggest reinforcing protection policies in fast patches to dampen the effects of perturbations and promote the stability of population dynamics at the regional scale.