Hi Brian, What you are experiencing is the same effect as when you see "cat's eyes" on the road. Cat's eyes bounce light back roughly in the direction it came and an insects eye is a 'compound', multi-faceted structure - basically it looks like a lot of tiny cat's eyes glued together in a rough hemisphere shape.
So the ring-flash is mounted around the lens and sends out a pulse of light towards the moth ... when it hits the moth's eyes the light travels down the facets that are facing towards the flash and the light bounces back out again towards the lens/ring-flash - giving that strange glowing look. But it just ricochets off the facets that point away from the flash and they appear brown.
As Rob said, the only way to avoid this is to mount the flash to the side of the lens so that the bounced flash-light doesn't come back into the lens.
