Is this iris transillumination or just my cheap camera?

Camera: If you are referring to "red eye" when you use your flash, it is most likely not iris transillumination. Transillumination is when light can pass through the iris. When you take a picture in the dark, people's pupils are dilated, so the light is bouncing back from the retina through the pupil, not the iris. Some cameras use multiple flashes to constrict the subject's pupil prior to taking the shot.

Probably the iris: If you are seeing light reflected back through what is ordinarily the solid donut ring of a normal iris, then it is probably transillumination. The cheapness of the camera is not an issue. The light pattern is and only a thin iris lets light getting to the back of the eye to come through the iris.