The only people who could notice time on the moving spaceship passing slower for Stella would be observers in an inertial, or non-accelerating, reference frame — like Terra back on Earth.
天文学百科 The Astronomy Book (Big Ideas Simply Explained)
If both observers were in the same reference frame, the described motion of the balls would occur because the balls had the same mass and were thrown with the same force.
Because as one pendulum is swinging, it provides the attachment point for the pendulum hanging below it, and so that pendulum is in this moving reference frame as it's swinging.
So it's basically the whole theory is built on the idea that these columns have reference frames, and we're learning these models, and these grid cells create these reference frames.