Actually, to take an alignment domain, you must match that alignment. (Under Deities, Domains, and Domain Spells on page 32 of the PHB.) But I don't see anything in that particular comic that demands Hilgya has the Chaos Domain, just Fire. Maybe if you'd clarify that...?
And opposites don't need to be completely opposite, so Hilgya does nto need to be Chaotic Evil (since Durkon is Lawful Good). Just opposite in some important ways and alike in others. Hilgya and Durkon are the same race, for instance, while Haley and Sabine are different races. Haley is Chaotic Good, but Sabine is Chaotic Evil.