This question makes a number of different assumptions, most of which are wrong.
1. The biggest, as covered by Slarty's answer, is that an alien species would even use the same pigments that Earth species use.
It's a common misconception that evolution is a gradual progression to the most efficient solution to a problem. It's not. For a trait to exist in many or all Earth species doesn't mean that it was the best or only trait to provide the needed functionality. It just happened to be the one that some common ancestor ended up with, and wasn't ever enough of a hindrance to be selected away.
We don't even know if alien life will use DNA the same way Earth life does, much less melanin and other pigmentation.
2. Melanin is required for pigmentation.
You're probably aware that most tree leaves are green. You likely know why, too. (If you don't, I'll give you a hint. It's not melanin.) Fish have three different pigments, Erythrin, Melanin, and Xanthrin. Birds use carotenoids, melanins, and porphyrins. Just because a species doesn't have any melanin, doesn't mean it has no pigmentation at all.
3. The presence of pigmentation is binary, either you have it or you don't.
You're probably familiar with the term albino, for a person or animal with a total lack of pigmentation. But there's a much less commonly known trait called leucism, where an animal will only partially lack their natural pigmentation. Sometimes this just means that their eyes are blue instead of pink, but it can also lead to some stunning piebald effects
4. Blue or red eyes necessarily means a lack of pigmentation elsewhere
And now I bring you the Blue-eyed black lemur, which naturally has shockingly blue eyes despite a black or tan fur coloration. Similarly, the red-eyed tree frog has (you guessed it!) brilliant red eyes.
The natural world is full of variations and exceptions. Never assume that just because two traits are commonly associated, that they are always related. You might as well say that all winged animals are birds, or that all vertebrates have spines. There's always an exception.