The recent surge of earthquakes in the central United States is linked to the disposal of large volumes of wastewater. Even if injection rates have been decreasing since 2015, the seismic hazard remains elevated. Moreover, some events in Kansas occur far from disposal wells. We applied a multidimensional cross‐correlation technique to analyze the spatiotemporal relation between fluid injection and earthquakes. While a strong correlation is observed in east‐northeastern direction of the disposal wells for the majority of events, some earthquakes occur in northeastern direction far from the disposal wells. We explain this pattern and the large‐scale evolution of borehole pressure observations by directional migration of poroelastic stresses and pore pressure diffusion. This follows from our principal 2D poroelastic finite‐element model that has a predicting power and identifies controlling parameters of the process. These are the permeability of the basement and its anisotropic character as well as the distribution of critical fault strengths. Our results suggest that remote locations may be destabilized even when injection rates are declining. Thus, a volume reduction may only provide an immediate effect to lower the seismicity locally. It follows that a state‐wide reduction in earthquakes may require longer waiting times and that the hazard of induced seismicity may remain elevated for tens of years.