To me, one of the things that identifies a better dancer, especially with a style like apilado, is how well defined my partner's axis is. I think it's no coincidence that someone like Laure Haile, who was dance director for Arthur Murray studios in the 50s, and documented "Western Swing" addressed the question of simply taking a step. Many of these things relate to most partner dances.
So, my partner and I take a step. If she establishes her "axis," that is, a clear line between her grounded foot on the floor, and her "center," and I can feel that in her body, and there is no momentum there, I know she is available to move in any direction. Or, she will very likely not move off that spot unless I lead further movement where there is no rotation involved.
Both partners, I think, cooperate to make things work. I think there is always more or less "wobble" in that a vertical axis through through the body won't be 100% vertical 100% of the time as we rotate. The more accomplished dancers understand that, and compensate for each other. (Course the better they are, the less they have to compensate!)
Hope that makes it more clear.