I don’t think that these visuals can be explained like that. I don’t think that in saddle shaped universe there is difference between one place from the other. These visualisations should be interpreted as every single part of the universe behaving like saddle shaped universe, for example. Or any other for that matter.
Also the representation of gravity pit is only a third of the story, to say so. It is a tridimensional depression, it pulls from all sides. That picture specifically is a bad one as you don’t see the effect that would be exerted on Earth to be in circular motion. It’s more like a sheet of cloth stretched and when you put a big ball in center it pulls all the marbles from the sides. I’ve seen that from some famous professor, name escapes me now.
However these shapes of the universe should not be interpreted as the actual saddle or flat plane, but rather as a description of it’s behaviour at each point.
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