Electrosprays routinely create sub-micron droplets containing functional molecules and show promise as a drop-on-demand dispensing method in the life sciences and materials processing. To precisely eject minute liquid volumes electrosprays must be turned on for milliseconds or less in the cone-jet or high-frequency pulsation mode. This work reports sequential phenomena which occur when electrosprays are triggered by sudden voltage steps. For low voltages the electrospray enters the pulsation mode but the pulsation frequency increases towards an asymptote, which increases with voltage. For higher voltages the asymptotic frequency is above a critical value and the electrospray switches to the cone-jet mode; after this the ejection rate increases until finally reaching a steady state. The total delay involves these phenomena plus the delay in forming a liquid cone; the latter depends strongly on both the initial and final voltage. The final electric field that must be applied is smaller when the electric field the liquid is subjected to initially is small—it is proposed that the inertia of a dynamically forming cone plays a role in lowering the voltage needed.