In astronomy we have the Aurora Australis in the south and the Aurora Borealis in the north. According to Wikipedia, auster is in fact the Latin equivalent of the Greek νότος, or southern wind. However, boreas is a Greek word, βορέας, not Latin! The Latin equivalent is aquilo. So, are the "southern lights" derived from a Latin word whereas the "northern lights" are derived from a Greek word? I can think of other places where auster/boreas are used as south/north. I find it unusual that this common pair would be derived from two different languages. How did this convention arise?
The term "aurora borealis" was arguably first used by a French scientist Petrus Gassendus aka Pierre Gassendi in 1621, in his treatise "Physics." For further discussion, see Siscoe, George. 1986. An historical footnote on the origin of 'Aurora Borealis.' In History of geophysics, volume 2
The phenomenon itself has been known for a long time in Europe; for example, the ancient Greeks called it "blazing skies" or "flaming sky dragons" (Hesiod, Theogony).
The term "aurora australis" was arguably first used in 1741 (OED)
Notice that when those terms were coined, they were used as Latin words. In other words, the Latin word "borealis" was used, not the name of a Greek god.
Common sense guess: The northern lights have been known in the west for a much longer time than the southern lights. Maybe the ancient greeks themselves knew of it and named it. The southern lights were discovered (by the west), and thus named, much later, by people who had neither greek nor latin as their first language. Maybe they didn't see a problem in mixing greek and latin terms.
Notice how many of the older scientific terms for animals and plants are a mishmash of greek and latin (now they are a mishmash of just about anything). If following that tradition, a mix of greek and latin to describe another natural phenomenon is perfectly understandable.