The propensity for dynamic earthquake triggering is thought to depend on the local stress state and amplitude of the stress perturbation. However, the nature of this dependency has not been confirmed within a single crustal volume. Here, we show that at Sierra Negra volcano, Galápagos Islands, the intensity of dynamically triggered earthquakes increased as inflation of a magma reservoir elevated the stress state. The perturbation of short-term seismicity within teleseismic surface waves also increased with peak dynamic strain. Following rapid coeruptive subsidence and reduction in stress and background seismicity rates, equivalent dynamic strains no longer triggered detectable seismicity. These findings offer direct constraints on the primary controls on dynamic triggering and suggest that the response to dynamic stresses may help constrain the evolution of volcanic unrest.