Dynamic triggering of earthquakes has been reported at various fault systems. The triggered earthquakes are thought to be caused either directly by dynamic stress changes due to the passing seismic waves, or indirectly by other nonlinear processes that are initiated by the passing waves. Distinguishing these physical mechanisms is difficult because of the general lack of high‐resolution earthquake catalogs and robust means to quantitatively evaluate triggering responses, particularly, delayed responses. Here we use the high‐resolution Quake Template Matching catalog in Southern California to systematically evaluate teleseismic dynamic triggering patterns in the San Jacinto Fault Zone and the Salton Sea Geothermal Field from 2008 to 2017. We develop a new statistical approach to identify triggered cases, finding that approximately 1 out of every 5 global M_w ≥ 6 earthquakes dynamically trigger microearthquakes in Southern California. The triggering responses include both instantaneous and delayed triggering, showing a highly heterogeneous pattern and indicating possible evolving triggering thresholds. We do not observe a clear peak ground velocity triggering threshold that can differentiate triggering earthquakes from non‐triggering events, but there are subtle differences in the frequency content that may possibly differentiate the earthquakes. In contrast to the depth distribution of background seismicity, the identified triggered earthquakes tend to concentrate at the edges of the seismogenic zones. Although instantaneously triggered earthquakes are likely a result of dynamic Coulomb stress changes, the cases of delayed dynamic triggering are best explained by nonlinear triggering processes, including cyclic material fatigue, accelerated transient creep, and stochastic frictional heterogeneities.