High-field THz sources with peak field strengths exceeding MV/cm are essential for nonlinear THz spectroscopy and coherent control of matter on ultrafast time scales. Two-color femtosecond laser plasma sources employing long filamentation have been reported as providing single-cycle, >MV/cm fields, with multi-decade spanning bandwidth and polarization control, making them promising sources for such experiments. In this work, we report the observation of spatiotemporal spreading of the THz pulse when standard off-axis parabolic mirrors are used for collection and focusing of long filament plasma-based THz pulses. This produces a flying focus for THz light, with the axial focal region propagating at a velocity of 1/3 the speed of light. The THz emission is then subsequently spread over a temporal width of ∼10 ps, approximately 100 times the THz pulse duration detected by electro-optic sampling at any single point along the focus. The consequences of this non-ideal focusing are a potential and drastic overestimation of the peak THz electric field based on energy measurements, as well as significant phase noise arising from beam pointing fluctuations. We show that this spatiotemporal spreading can be minimized using a simple axicon lens that perfectly collimates the extended filament source, resulting in improved spatial and temporal focusing of the THz pulse.