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I think it's likely that these "white" eyes are found in the males only. You'll notice that the facets are much bigger than in the coloured part of the eyes below. Many male tabanids have larger facets in the upper part of the eyes, and I suspect that when the facets get really big, they tend to look white. Females have more evenly-sized facets, and the eyes tend to be unicolorous (apart from the spots or bands, of course).
Not sure why males have these enlarged facets - presumably to help them find a mate, but how it is an advantage to have less visual accuity, I don't know.