We theoretically examine the spatiotemporal evolution of near-field optical chirality (OC) in both plasmonic and dielectric nanospheres when excited by ultrashort optical pulses. We demonstrate distinct spatiotemporal variations in the near-field OC arising from the differing natures of plasmonic and dielectric resonators. The electric dipole resonant plasmonic nanosphere generates an instantaneous near-field OC that relies on the interference between incident and scattered (induced) fields. Conversely, a resonant dielectric nanosphere sustains a long-lasting OC even after the incident field vanishes, due to the scattered field from resonant electric and magnetic dipoles. We further demonstrate the control over the near-field OC using vector beams to tune electric and magnetic mode excitations. Our work opens up opportunities for spatiotemporal control of nanostructure-enhanced chiral light-matter interactions.