Without seeing the photos in question, I can't give you an exact answer. My best guess is that your flash was too far away to cause red-eye but was instead reflected from the moist surface of the eyeball as a white catch-light right in the center of the eyeball.
However, I can give you some tips on how to shoot photos in this situation.
First, flash and telephoto lenses do not work well together. The reason for this is that the light provided by your flash falls off dramatically as the distance increases. This is called the Inverse Square Law
. What happens is that the light provided by your flash at 10 feet is 1/4 the light provided when the subject is at 5 feet - not 1/2 the light as you might first suspect. For this reason flash becomes essentially useless when your subject is more than 15-20 feet from the flash. Unless you can put strobe lighting on the stage and trigger it remotely from your camera (a very expensive process), you need to shoot with the available light.
First you need "fast glass" - this means a lens with a small f-stop number when zoomed to the maximum telephoto distance. These lenses are heavy, and expensive, but this is what you need to use to get this job done. Let me know if you want a link to some sites that rent these lenses. You need to shoot at the widest aperture (minimum f-stop number). I shoot with a 70-200 lens at f2.8 for this type of situation. Shoot in Aperture Priority mode so you can set the f-stop to the minimum for the lens (e.g. f2.8).
Second, you need to bump the ISO to the highest setting. This is why digital cameras have a high ISO setting, to enable you to shoot in low light. The images are going to have a lot of noise but there's no way around it - this is part of low light photography. Don't forget to reset the ISO after your are done - you don't want to shoot in high ISO all the time - just use it in low light situations.
Third, I usually under-expose by 1 stop so that I can use a shutter that is 1-stop faster than I could use otherwise - to minimize motion blur. This can be done in Aperture Priority mode by setting Exposure Compensation to -1. The shots will be a little dark but I find that it works OK because they "look" like they are on stage this way. You can also lighten them a bit in the post processing. If the light is really, really dim I may even shoot at -2.
Fourth, only shoot when your subject is in the brightest areas of the stage - don't try to get a shot when your subject is off on the side in dimmer light.
Fifth, shoot in RAW. You can do a lot in post-processing of RAW files to bring out details and minimize noise. If you shoot in JPEG there is little you can do to fix these problems in your post-processing.
Finally, you need to either use a lens with IS or VR that helps minimize blur from camera shake, or you need to use a tripod or monopod to help stabilize the camera.