At first I didn't see a cylinder - I was focusing on the middle of picture and seen 2 "rivers" - white going one way, black another way. I could decide which "river" is in front by focusing on either black or white dots. So I would probably "pass" the test - my pupils must have react to the color of dots I was currently focusing at.
After looking at the picture for a while I found the cylinder (I think so at least - by cylinder you mean dots moving in rounds, right?), with either white or black dots in the front of my choice. The cylinder seems to also be changing direction according to my will - I can do the same thing with the spinning dancer illusion
https://en.wikipedia.org/wiki/Spinning_Dancer .
Then I looked away and looked at the picture again. Now my focus stopped at the edge first and I could suddenly see dots bouncing off it and changing colors as they do. It was pretty overwhelming - I tried to track all of them and 3 dots going in the middle pissed me off - the gif is ending before they hit the edge!
Then I started playing by switching my focus between bouncing, rivers and the cylinder changing direction as I want it to.
In both cases "cylinder" wasn't what I could see at first, but I found it eventually and could control it then, by choosing which dots to focus on.

BTW. If people literally see "a spinning hollow cylinder, black on one side and white on the other, randomly changing direction" they must be nuts... It can't be literal, can it? The cylinder is gray with black dots on one side and white on the other at best.
The fact that the OP mentioned the word cylinder might have been a "spoiler", but...
To me it just jumps out as being a slowly turning cylinder. I did not notice it change direction. The close side moved right to left always. The dots give the cylinder texture (crusty and rusty). The white dots look like light glinting off a wet surface. So it looks like a rusty iron pipe just pulled up out of the ocean. You can switch gears and see it as dots moving majestically in a choreographed ballet as well. But NOT seeing the cylinder takes work.