This work presents evidence of the relation between the dynamics of intense events in the dissipative range of turbulence and the energy cascade. The generalised (Hölder) means are used to construct signals that track the temporal evolution of intense enstrophy and dissipation events in direct numerical simulations of isotropic turbulence. These signals are remarkably time-correlated with the average dissipation signal, and with its large-scale surrogate, despite describing only a small fraction of the flow domain, and they precede the dissipation signal with a temporal advancement that grows with their intensity and that scales in integral time units. Interpreted from a causal perspective, these results point to the energy cascade as the driver of the intense events in the dissipative range. Moreover, it is shown that the temporal advancements of the generalised means are consistent with a local energy cascade, whereby eddies cascade in a time proportional to their turnover time, causing intense eddies to reach the dissipative scales before weak eddies. These results shed light on the dynamics of intense and extreme events in small-scale turbulence, and provide empirical support to the phenomenological foundations of a broad class of intermittency models based on the turbulence cascade.