I'm unclear on pretty much all the details surrounding the issue as you described it, and I'm guessing I'm not alone on that.

When you say "it worked outside of vMix", what exactly do you mean?

When you say "the moment they got onto vMix", what exactly do you mean?

Your title indicates that the problem occurs when they turn on the ring light, but your post says it happened "the moment they got onto vMix". Those are two entirely different things.

So I'd suggest going back & starting at the beginning, but, this time, with actual detail about what happened, when it happened, and when it didn't happen.

As it stands now, I can't make heads or tails out of it.

My first thought, which may or may not be contradicted by your post, is that if the light was USB powered (which I don't know, because you didn't say one way or the other) & if the microphone was USB powered (which I don't know, because you didn't say one way or the other) & if they were both connected to the same port via a hub (which I don't know, because you didn't say one way or the other), then it's possible that the hub or port wasn't delivering enough power for both.

Or there could be a driver issue of some sort.

Or some sort of short in something.

Or anything else that I can't even begin to say because I don't even understand the nature of the problem.

Or it could be a coincidence, because you never said one way or the other if the audio came back on when the light was turned off or if the computer was rebooted.