Were they dyed or were they fake or both? Dyed and "fake"/natural (I am assuming you mean either synthetic or imitation here) are not the same thing.

Dying is a treatment. Granted it should be disclosed to you, but it is not technically incorrect to describe a natural (created by the earth and mined) stone which has been dyed as genuine and natural. To say it's untreated would be a lie.

If the stones are lab-grown calling them natural is fraudulent. They would actually be synthetic. If they are a completely different material than what is claimed, not disclosing that they are "imitation" is fraudulent.

It's important, when buying gemstones, to understand the terminology the industry uses and its nuances of meaning. I cant really tell from your post if you are saying they are not the stone they claim to be, or if they are just treated and you weren't expecting that.

Give her a couple days to respond. Refunds can also take some time to post, so that's something to keep in mind. If she's still unresponsive, then go ahead and open a case and let Etsy sort it out.