The results of numerical simulations of the generation of runaway electrons in a nitrogen-filled coaxial diode with electron emission governed by field emission that transfers to explosive emission with a variable time delay are presented. It is shown that the time when the explosive emission turns on influences significantly the generation of runaway electrons. Namely, an explosive emission turn-on prior to the formation of the virtual cathode leads to an increase in the current amplitude of the runaway electrons and a decrease in its duration. Conversely, an explosive emission turn-on after the formation of the virtual cathode and during the high-voltage pulse rise time does not influence the generation of runaway electrons significantly. When the explosive emission turns on during the fall of the high-voltage pulse and after the virtual cathode formation, one obtains additional runaway electron generation. Finally, a comparison between electron energy distributions obtained with and without explosive emission turn-on showed that the former increases the number of electrons in the high-energy tail and the electrons' largest energy. The comparison of both the simulated electron energy distributions with the experimentally obtained electron spectrum has shown that the best fit is obtained when the explosive emission is considered in the simulation.