Abstract Many collective phenomena such as epidemic spreading and cascading failures in socioeconomic systems on networks are caused by perturbations of the dynamics. How perturbations propagate through networks, impact and disrupt their functions may depend on the network, the type and location of the perturbation as well as the spreading dynamics. Previous work has analyzed the retardation effects of the nodes along the propagation paths, suggesting a few transient propagation "scaling” regimes as a function of the nodes’ degree, but regardless of motifs such as triangles. Yet, empirical networks consist of motifs enabling the proper functioning of the system. Here, we show that basic motifs along the propagation path jointly determine the previously proposed scaling regimes of distance-limited propagation and degree-limited propagation, or even cease their existence. Our results suggest a radical departure from these scaling regimes and provide a deeper understanding of the interplay of self-dynamics, interaction dynamics, and topological properties.