When Albert accelerates the second time, he experiences a large speed change relative to Rick, while speed change relative to stars is smaller. Also direction of light coming from Rick changes a lot, while direction of light coming from stars changes less.
When stars accelerate and Albert stays still, Albert can say that there is an aberration effect in the light coming from the stars. In my opinion this is not a relativistic effect, for the same reason that a car driving at 50 mph does not have a relativistic effect on a radar beam, it is too large an effect to be a relativistic effect.
Let us consider a laser pointer, pointing into unchanging direction, accelerated two times. The second acceleration causes a smaller change of direction of the laser beam compared to the first acceleration.
Let us consider a laser pointer accelerated two times, after the first acceleration we turn the pointer so that the beam is NOT turned. Now the second acceleration causes the same amount of turning of the beam as the first acceleration.
Oh yes the first case is incorrect if the pointer points backwards.
This is a good explanation