The OP requires: "No speculation please". I would say, this is a tall order. As there are no other answers so far, I would like to try to answer, but I cannot promise I will be able to do without speculations, as we don't have much information.
Let me start with the following note. The discharge area remains white, and it is the periphery of the discharge that acquires different colors. To demonstrate that, I made a couple of screenshots from the video, cropped them, and then replaced white pixels with black ones (in Mathematica).
Cropped image with red periphery:
Same image with replaced white pixels:
Cropped image with green periphery:
Same image with replaced white pixels:
So what is the mechanism through which the discharge affects its periphery, sometimes at a significant distance from it? I suspect that it is photoionization. Electrons in the discharge can acquire significant kinetic energy in the electric field, generate bremsstrahlung (with energy of dozens eV or higher) in collisions with atoms, the bremsstrahlung photoionizes atoms (within the discharge, but also on its periphery), and then electron transitions in the ionized atoms (on the periphery, it is mostly oxygen and nitrogen atoms) cause radiation at characteristic atomic frequencies (see, e.g. [1] and [2]). Within the discharge itself all colors are saturated, resulting in white color.
Let me try to answer a couple of questions.
Why does not burning magnesium color the periphery? Because electrons do not acquire sufficient energy without external electromagnetic field (the temperature of magnesium flame is about 2500K, which corresponds to something less than 0.3eV).
Why do the colors on the periphery change? I don't have a clear idea, but let me note that there is obvious instability of the discharge in the video, which probably can cause some relatively slow color changes.