Applet 2 (ref: Corrections/ Additions - Footnote 7)

In the second (more inclusive) applet, the lines in the circles (which seem to denote amplitude of that stationary state) are shown to be rotating. What is the rotation for.
I first thought that the rotation stands for the changing phase, because after all, before we start the timer (by uncchecking the 'stopped' box), relative phase differences can be adjusted by rotating these lines inside the circles.
However, if they did stand for the phase, then shouldn't the second stationary state's phase increase 4 times as rapidly as that of the first? The phase factor is directly proportional to E<n>, and E<n>, the energy of the nth stationary state is directly proportional to n^2!

Or otherwise, can you please give a probable explanation?