At first, I thought that the color was simply draining from her face in a literal sense upon seeing Raven and that it was meant to be comical, but now I think it's definitely too specific, given the importance of silver eyes thus far, for it to simply be a joke.
I don't however, think that Neo is related in any way to Yang or Raven. As we've seen in Vol. 4, Weiss' butler, Klein, can also change eye color in accordance to his mood. Unless Klein is secretly Raven's father and thus Yang's long lost grandfather, this seems to be a fairly common trait.
Silver eyes, though, are not common at all, as we know. However, that does not mean that all silver eyes warriors must be directly related. While Ruby probably received the gift of silver eyes from her mother, who's to say that Summer was the only Silver-eyed Warrior left? It seems to me as though there was once a clan of them, and that they have descendants, such as Summer, Ruby, and, very possibly, Neo.
While writing this, I had an epiphany, if one could call it that. More of a random thought that, upon thinking about it, makes a bit more sense than simple coincidence.
Think back to the opening for Volume 3. Towards the end, whilst the main characters spiral downwards to display their helplessness, a familiar red void appears. This same void seems all too similar to the portal that Raven uses to teleport. It must have some sort of meaning, and I thought that Raven may make an appearance. She did not, though, so it must mean something else.
A character that did appear a few times, however, was Neo. The last of which being when she was elected from Ironwood's airship by Ruby before Torchwick died, never to be seen again in that or the next Volume. Why introduce such an interesting character and leave her fight with Yang unsettled only to not show her for a whole season? All of the other characters were shown, even supposedly dead Ozpin, Professors Port, Oobleck and Glynda, and of course, Raven.
And then it hit me: during Raven's talk with Qrow in Vol. 4, Qrow implies that someone new and powerful was taken in by Raven's group. This was the first we heard of this group, and still don't know much about it, but it must be important that someone capable of destroying villages was added to their numbers. The fact that this addition occurs after Neo's disappearance, as well as her obvious skill in combat, would suggest that she might be this mystery member. Given that Ruby managed to freeze the Dragon Grimm and almost kill Cinder with her silver eyed power, Neo would be plenty strong enough to take out villages outside of the kingdoms, especially if she knew how to use her abilities. Of course, if Neo were scared of Raven, then it wouldn't make sense that she would go to her group willingly, would it?
Unless, of course, she were already a part of that group.
Humor me, for a moment, as I recall the fight between Team RWBY and Torchwick's Mech. After Torchwick has been defeated, Neo saves him, making her fist appearance in the show. Given that Yang points out that she's a "new henchman," this must have been the first time she's helped Torchwick as well.
But why join such a street rat? I refuse to believe that she was just thrown in to make things interesting. She must have come from somewhere, and believe that somewhere is the mysterious group led by Raven.
Raven obviously knows of and is opposed to Salem. It would make sense that she would send a spy to infiltrate her ranks from the easiest point of entry: as a mercenary, hired by Torchwick. The reason she seemed afraid of Raven, and why she flashed her silver eyes, was because she wasn't sure that Raven would recognize her disguise as the Neo that we all know, and that she might kill her. Once she saw that Raven was still intent upon saving Yang, she left, never to finish the job, because Raven is her leader. After Torchwick dies, Neo returns to Raven.
When Raven leaves Qrow in the bar in Vol. 4 via the red void, the waitress was visibly afraid of the sight of it. Qrow's nonchalance about her reaction seems to imply that it's a common for people to be afraid of it, and, given the implication that Raven's group destroyed Shion village, it's probably because it's their known symbol. The appearance of it in Vol. 3's opening is meant to symbolize Neo returning to the group after the Fall of Beacon, possibly with information about this "artifact" everyone's so worried about.
TL;DR Neo is a spy, sent by Raven, to infiltrate Salem's forces.