This from Sigma:
Autofocus tuned for each lens
Thanks to an autofocus drive control program tuned for each lens and high-speed data transmission, the lenses will offer high-speed autofocus at the same performance level as that of a lens designed exclusively for mirrorless cameras. In particular, in E-mount cameras offering Sony’s Fast Hybrid AF, AF-C mode will deliver exceptional subject following performance. Moreover, autofocus will remain extremely precise even in those E-mount cameras offering only contrast AF.
I only started shooting today, so can’t say how fast video AF-C is just yet.