Actually just figured this out, in case anyone sees it. They are dictated by the color of the action bar on the conversation screen, which also controls the contact circle background color for people who don't have an image. Tested it by changing a few different items to random colors and spamming myself with texts.

YES! I came here to post this. I have a dark blue and red theme that I really like, but thinking of changing it due to this.

On my old phone, HTC One M8, the dots showed up red, which aligned with some of the colors I selected. I can't remember if there was a specific setting for it or not. Unfortunately I can't check, cause that phone is dead. But maybe it depends on specific version?