As concerns rise over damaging earthquakes related to industrial activities such as hydraulic fracturing, geothermal energy extraction and wastewater disposal, it is essential to understand how subsurface fluid injection triggers seismicity even in distant regions where pore pressure diffusion cannot reach. Previous studies suggested long-range poroelastic stressing and aseismic slip as potential triggering mechanisms. In this study, we show that significant stress transfer originating from injection-induced aseismic slip can travel at much higher speeds and is a viable mechanism for distant earthquake triggering. It could also explain microseismicity migration that is much faster than aseismic slip front propagation. We demonstrate the application of these concepts with seismicity triggered by hydraulic fracturing operations in Weiyuan Shale Gas Field, China. The speed of stress transfer is dependent on the background stress level and injection rate, and can be almost an order of magnitude higher than that of the aseismic slip front.