The entire top of the towers were filled with your dark smoke. When A volume of smoke in a cube an acre square by about 240 feet high is compressed during a collapse. Where do you suppose the smoke goes?
First of all, we are supposed to believe that the "cube" remained relatively intact and crushed down through the undamaged lowere structure. (see Greening). So if you believe that, then you don't have a compressing cube at all.
Ignoring that, it is the change in behavior of the smoke that you must consider. It goes from lazily drifting upwards and to the southeast, to mushrooming outwards in all directions and growing rapidly. This requires an energy input.
If the building is falling, then the floors are falling, and the fire is falling, and the source of the smoke is falling. This would tend to make it go down, not up. The space formerly occupied by the building will have low air pressure, thus pulling smoke down toward it, again down.
Clearly we observe something is creating great pressure sideways. I say it is massive explosions of some sort, you would say it is compression from falling mass, redirected sideways. In either case, this force moves sideways and expells huge amounts of material sideways, not up.
Other than a large source of new heat that was not present in the moments before the event, we have no explanation for the change in the behaviour of the smoke.