To trigger a flash tube, a very large voltage is needed to ionise the gas. That is usually capacitively connected by a wire around the outside of the tube and the voltage comes from a pulse transformer. In cheap flashes the capacitor is directly connected to the tube, and there is nothing to stop the arc so it carries on until the capacitor is discharged.
To stop the light, the current has to be stopped. That was done with a thyristor and a commutator circuit . I don't know if there are better technologies now. I guess that a Gate Turn Off, or GTO thyristor, would be used.