Two examples of possible time dilation based on reference frames and acceleration:
An alien ship flies into our galaxy. They watch the arms spinning (assume they are immortal and have a LOT of time to spare). One alien says "I think I'll ride around the galaxy on one of those arms once. The other says "go ahead, I'll wait here". So Alien 1 ejects in a pod and accelerates to match the arm speed of the galaxy. He loops once around, then slows down in order to board his ship again. In this example my assumption is that the alien that accelerated and decelerated (alien 1) had less time elapsed than the alien who was stationary. Their reference point could be the center of the galaxy as the ship is in the galaxy but not rotating with it.
Humans evolve into immortal robots. One of these cyborgs does the opposite as alien 1. He accelerates away from earth to travel at the speed the galaxy rotates. Earth (really the sun) spins around the galaxy once. He decelerates relative to earth and lands on earth again. In this case, time should go slower for this cyborg because he is the one doing the acceleration. His reference point is earth.
What's the difference between #1 and #2. Seems to me the cyborg is the same as alien 2 while the people on earth are the same as alien 1. Yet in the examples it's the opposite entities doing the accelerating.
What's wrong with this? Which of my reference frames is wrong?