I can't remember the time it took in (split) seconds for the top of the slinky to make its way to the bottom without watching the video again, but that seems to be the key.
Slo-mo plays with our minds a bit. The bottom does move, but not until the top reaches a "critical mass" point. The bottom is connected to the top, after all.
The slinky is a whole object, but its mass is "spread out" by design, the physicists discuss this - the same thing happens with a "solid" object (say, a lead bar), just quicker.
Like I said, my math skills are mediocre.
The red dot on the moving chart is supposed to represent where the center of mass is moving. The blue on the spring represents the compressed part.