The red-eye is caused by the colour of the iris which controls the diameter of the pupil. Only some diving birds have red irises, try seeing the eye of a King Penguin in a photograph, it is usually impossible to see because the iris is black and it is buried among black plumage. It is this contrast with the plumage or skin colouration around the eye that gives away the function of eye colour. It is used as a signal and does not have any effect on vision (whether in air or in water). The pigmentaiton of the iris is just a device for making the iris as opaque as possible in order to accurately control the amount of light reaching the retinal. i.e. no light leaks in through the iris muscles.  Eye colour was extensively reviewed by Mann in 1931 when it was conlcuded that iris colour is used as a signal between animals and there has been no evidence to counter this conclusion since. So that a structure used for signaling is conspicuous it needs to contrast with its surroundings and so bright iris colours often contrast strongly with the feather or skin of the head in birds. The idea that diving birds tend to have red eyes is probbaly just a sampling error. There are grebes with yellow eyes, penguins with black, red and yellow eyes, cormornants with blue, green, red and black eyes. It is also worth noting that iris colour changes with age in many birds with young birds showing only browns and blacks and full bright colour achieved only in adulthood , presumably this is when the need to use iris colour as a signal of fitness or emotional state becomes important.