To elucidate the role of dispersion in electromagnetic phenomena within bounded dynamic media, we investigate the scattering of an electromagnetic wave by the rapid creation of a dispersive Lorentzian medium in a half-space. Two creation regimes are considered—instantaneous and transient—classified according to the switching duration relative to the timescale of the medium’s intrinsic resonant oscillations. The applicability of the conventional model of a nondispersive dielectric with a time-varying permittivity is examined for each regime. Our results reveal that transient radiation plays a significant role in both scenarios, and is essential for preserving electric field continuity across the spatial interface.