The way the rebar is threaded through and around the central steel beams in the most recent photos, it looks like they're pouring concrete directly around those steel beams.
So it seems that the base of the core is a combo of steel beams and concrete, not just one or the other. So obviously they'd need to get the steel in place first. And any steel that ties directly into it affects flex and stresses; better to get that all connected and stable as a system before pouring any concrete. (Said as a complete non-engineer, so I really have no idea.)