It makes sense. As the two stars oscillate away from the mean center of the ellipse, they correct any chance for the orbiting satellite to drift out of the perpendicular too far. So I would imagine you would see a wobble (or tilting back and fourth) measured greatest at the apogee of the ellipse, but the swing is always back or corrected to the mean.
Orbital mechanics truly is fascinating. There are so many bodies in our solar system, I’m surprised we don’t see more collisions. Shoemaker-Levy 9 was a rare, spectacular event.