Causality is defined in the link---> (d < dH). The distance between 2 points is less than the light horizon. It is obvious that the horizon expands at the speed of light. Therefore, if an object is at a distance less than that horizon(within the light cone of the other object) at any time it must travel faster than the horizon's velocity to be greater than the horizon(outside the light cone); that is, from this (d < dH) to this (d > dH).(it must do so while within the horizon--the superluminal velocity). Explicitly, if a distance grew(separated) 1 mm in 10-33 seconds, it would have to "travel" at least 1030 m/s during some portion of the growth. The speed of light is somewhat slower than that.
All of this using a given Universal Time Zone, a specified absolute T.(Hey, I'm not the one specifying T, it's the inflation guys and their timeline.)
Causality means that causes always precede effects. Do you understand why d < dH is equivalent?
It is obvious that the horizon expands at the speed of light.
As a matter of fact, during inflation the horizon shrinks.