RE: WIX 57061 Oil Filter VS. Hyundai Oil Filter
That's the cartridge filter, right? I don't really know much about those.
For the standard screw-on base filters, there was an issue with aftermarket filters not having the correct specs which led to oil starvation. Most commonly it seemed that Fram was the culprit; the reputation for "good" aftermarket filters seemed to be that Wix and Purolator were okay.
In that case, though, I think it had more to do with the pressure of the bypass valve. Honda and Hyundai used the same screw-on base, and Honda has a higher trip point for the bypass valve, which means that if a Honda-spec filter was used on a Hyundai, it wouldn't bypass until a higher pressure than required and the engine would suffer damage from oil starvation.
I'm not sure how any of that applies to cartridge filters though.