When an event is detected, the warhead shuts down its electronics for the duration of the EMP, and then powers back up.
I doubt this, since the EMP is moving at the speed of light, whereas the delay times inherent in most circuitry and the time required to power down most circuitry would be at least an order of magnitude (most likely more) larger.
Why does the rate of propagation matter? I presume that during the course of the explosion there are several sequential phases. If phase x emits some non-EMP but detectable signal, say an X-Ray burst and phase y emits the EMP, both of which propagate at the same rate, then you have time(y) - time(x) to respond to detecting x before the EMP from y reaches you.
Explosions, like all other macro scale phenomena are not instantaneous, they just appear so until an appropriately small time step is applied.