Based on the Tiburon's age, you'll probably see different recommendations out there just based on what the current Hyundai spec is...which in my opinion isn't what I'd put in it. As others have said, I'd use something akin to Redline MT-90 or the equivalent 75w-90 Amsoil or similar product.
I believe Redline recommends 75w85 ( MT-85 ) which is what I have in my '13 Accent and Amsoil recommends a 75w-90 product. I'd defer to the 75w-90 just based on the original spec and would probably have a preference for Redline ( having used MT-90, MT-85, and MTF in years past ) . A good GL-4 specific fluid ( a relative rarity ) would probably suffice, but I think that makes it a choice between Amsoil, Redline, and a couple others.