With key in "RUN" position, the ASD relay will energize the pump to prime the fuel system prior to cranking. You should hear the pump run when cycling from "OFF" to "RUN".
Otherwise, we have had mulitple cases where an aftermarket crank sensor did not function out of the box. For that reason, we only use OE crank sensors. If the sensor is no good, the ASD won't provide voltage to the pump, ignition coil, or injectors during cranking.
Good luck