Video demonstration:

Great explanation by Redditor Mzsickness:

This machine is moving the fluid using laminar flow (good job op). This fluid has a very high viscosity (meaning it flows like honey) so the fluid doesn't move around a lot when set into motion.

This machine is not mixing the fluid at all. There is a difference between mixing and agitating. When you mix a fluid you're randomly distributing the particles around. In agitation you're moving the particles in a specific pattern.

Since the guy in the gif isn't mixing the fluid--he is able to agitate it in the reverse direction back to the fluids original spot.

If he did this with a lower viscosity fluid it would be almost impossible do due to the motions of the particles inducing a slight randomness to the fluid. But since there's a high viscosity the particles move very slow.

tl;dr This is possible, this gif is most likely not reversed. However, when they guy says "then the fluid is mixed" he's completely wrong and should be shunned by all scientists.