We study the shaping of pulsed two-dimensional optical beams by chiral sculptured thin films (STFs) in the time domain, so that the spatiotemporal evolution of the light is elucidated as it propagates through the film. The time-domain manifestation of the circular Bragg phenomenon is examined in two dimensions, and we comment on its implications for pulsed beam shaping by STF devices. Several crucial differences separate the time-domain manifestation of the circular Bragg phenomenon for pulsed plane waves and pulsed beams. Specifically, the beam waist is an important parameter for prediction of how reflection from or transmission through a chiral STF will shape the edges of a pulsed beam with respect to its central portion. In addition, control of the position of chiral STFs with respect to pulsed beam sources is important for proper pulse shaping. We expect that further advances in STF fabrication will allow for the development of STF-based pulsed beam shaping devices.