We study experimentally and numerically the spatiotemporal dynamics of the multiple filament arrays excited by self-focusing of intense elliptical laser beams in fused silica. Our results demonstrate that although multiple filament arrays emerge as apparently regular patterns in the space domain, the spatiotemporal dynamics of the individual filaments is governed by the input-beam power and the input-beam ellipticity. In the case of moderate input-beam ellipticity, the individual filaments propagate in curved trajectories arising from skewed (spatiotemporal) coherence. The spatiotemporal propagation dynamics is regularized by increasing the input-beam ellipticity, and in part due to permanent modifications of fused silica that occur under intense irradiation. In this case, strong pulse reshaping and shock-front generation are observed, which yields a regular array of very short ($<5$ fs) superluminally propagating localized peaks in the leading front, followed by the subpulses centered on the input-pulse top, and trailed by subluminally propagating pulses with rather complex transverse intensity distribution.