What Matt in the PBS Space Time video means by "reversing the direction of your changing spacetime interval" is to change the sign of Δs[sup]2[/sup]. For allowed (slower than light) motions, Δs[sup]2[/sup] is negative, while for faster than light motion, it is positive. Their diagram represents the negative values as being downhill while positive is uphill, which is a nice way to visually distinguish these different regions of spacetime and whether they are accessible or not. The boundary between them is where Δs[sup]2[/sup] = 0, which is level (neither up nor down), and can only be followed by photons.
Some more jargon: we refer to Δs[sup]2[/sup] < 0 as "time-like", Δs[sup]2[/sup] > 0 as "space-like", and Δs[sup]2[/sup] = 0 as "light-like" or "null". Everything on the diagram separated by "space-like" intervals is inaccessible since it would require moving faster than light, and we call that region "elsewhere", being outside of our light cone.
The downhill side opposite the direction of our future, is the direction to the past. It is our "past light cone", showing those events that have had causal influence over us.