Chiral sculptured thin films (STFs) have unidirectionally periodic electromagnetic constitutive properties and therefore exhibit the circular Bragg phenomenon. The time-domain Maxwell equations are solved using finite difference calculus in order to establish the spatiotemporal anatomy of the action of axially excited, chiral STF slabs on optical narrow-extent pulses (NEPs) modulating circularly polarized carrier waves. A Lorentzian model was adopted for the permittivity dyadics of the chiral STFs. The time-domain manifestation of the circular Bragg phenomenon is focussed on. First, on examining the refraction of NEPs by a chiral STF half-space, a light pipe and the pulse bleeding phenomenon are shown to occur -when the handednesses of the carrier wave and the chiral STF coincide and the carrier wavelength is in the vicinity of the center-wavelength of the Bragg regime. Next, pulse bleeding inside a chiral STF slab is shown to be responsible for the long wakes of reflected pulses and low energy contents of transmitted pulses, when the incident wave spectrums significantly overlap with the Bragg regime and the carrier waves have the same handedness as the chiral STF slab. Thus, a chiral STF slab can drastically affect the shapes, amplitudes, and spectral components of femtosecond pulses.