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Percolation theory is essential for understanding disease transmission patterns on the temporal mobility networks. However, the traditional approach of the percolation process can be inefficient when analysing a large-scale, dynamic network for an extended period. Not only is it time-consuming but it is also hard to identify the connected components. Recent studies demonstrate that spatial containers restrict mobility behaviour, described by a hierarchical topology of mobility networks. Here, we leverage crowd-sourced, large-scale human mobility data to construct temporal hierarchical networks composed of over 175 000 block groups in the USA. Each daily network contains mobility between block groups within a Metropolitan Statistical Area (MSA), and long-distance travels across the MSAs. We examine percolation on both levels and demonstrate the changes of network metrics and the connected components under the influence of COVID-19. The research reveals the presence of functional subunits even with high thresholds of mobility. Finally, we locate a set of recurrent critical links that divide components resulting in the separation of core MSAs. Our findings provide novel insights into understanding the dynamical community structure of mobility networks during disruptions and could contribute to more effective infectious disease control at multiple scales. This article is part of the theme issue ‘Data science approaches to infectious disease surveillance’.