Here's a gif showing it (the largest star on the right with the halo):

Let me walk through how this star, like the moving one, came to be.
I was going to make small star field, but I didn't want to make a whole bunch of stars with light blooms and have to animate each one by hand. So, I decided to make some template stars, animate them with actions, and then add reference layer groups to the project referencing those stars, and just plug in the animations where I wanted them. And for the first star it worked just fine.
I clicked on the star's Layer Folder, clicked in the action window and created a new action, named it, animated all the layers for the star, saved, inserted the reference layer group where I wanted it, and then inserted the action reference into the timeline. When I tested it in the editor window, it worked just fine. When I previewed the animation, via the File menu, it worked just fine. And when I finally exported the animation, all worked perfectly. "Alright good. Let me do that with the next star.", I thought.
Following all the steps I did to get the last one up and running, I created the new star (I call it quasar). And just like the last one, I added it to the project and tested the animation. In the editor window, it worked. In the animation preview, it worked. However, when I exported the animation, it would refuse to move. "Ok", I thought. "Well, maybe the action was too subtle for for me to see it. Alright", so I went back and edited the original star's action (not the reference), made the grow/shrink part of the action more pronounced, and tested again. Still the same effect: no movement.
I'm not sure what I'm doing wrong. Even the action animated like I wanted to. Can anyone help me out?
UPDATE: I plan to add a different video to this, showing the action and preview of the star.
Here it is: https://youtu.be/N3hv8aii_go