I've been looking for videos of the mixing effects and ran across this which may be enlightening. Not sure if it applies 100% but it was surprising how fast things mixed.
https://youtu.be/FE9VbiVbZFM?t=60It's not a direct comparison due to the difference in the aerator design but still interesting.
I'm now thinking of adding some pond blue to my deep aerator airline to see what happens.
That is a neat video, thanks for posting it.
I will say that putting dye in a pond, even without aeration, it disperses amazingly quickly. I was surprised at how quickly it spread throughout the whole surface.
But I would suspect it only dispersed (without aeration) only near the surface or at least above the thermocline. That is what the vertical pumping of water of the aeration system does. Mixes the different density cold lower water with the upper lighter warmer water.
If you go swimming and approach the diffuser, on mine about 10-15 feet away you can feel the cold water difference as the diffused plume of bubbles brings up the cold water and it disperses across the surface just like the video shows.
I think wind (or lack thereof) also plays a big role. With no wind that cold water that surfaces could have the inclination to drop again as it moves away from the diffuser plume. But with any wind at all the surface current will quickly move it away from the plume. It is surprising how many and much current there is in a pond created by wind and also just by the sun warming. Dye would work well to show the currents. Even mud will do it. Mix up some clay in water and dump it in some area and watch natural currents disperse it.