Hi jchar27,
Welcome to the forums! Take a look at my PSA regarding balancing the Hankook tires:
http://genesisowners.com/hyundai-genesis-forum/showthread.php?t=14856
Long story short the tires must be balanced when warmed up and then immediately lifted. If there is no vibration whatsoever after 5-10 minutes as you seem to indicate, this is normal for tires that are purely wrapped with nylon instead of a blend or another material entirely.
I don't think it's normal at all for a $50k luxury sedan to flatspot in as little as a few hours. I encourage you to give Hyundai USA at 800-633-5151 to report the issue. The other thread that Alwaysforward posted has more about my experience doing that. Again the TL;DR version is: the front line rep will tell you that you must contact Hankook as there is no warranty through Hyundai on the tires. Insist that even a new set would do the exact same thing (because it would,) and that you're debating Hyundai's choice. If they give you trouble still, they seem to be appropriately sensitive to comments regarding Hyundai caring about their Genesis customers.
Between my dealer's service manager being in touch with Hyundai and my experiences with a regional rep, it's fair to say Hyundai is aware of the problem but don't know how they're going to fix it yet.
For all I know they're just blowing me off, so personally I think it'd be really helpful if everyone with the issue could call in and start a case.
I've never had or even heard of a vehicle's tires flatspotting in a few hours or overnight, I think it's complete crap even on an economy car. Which a Genesis is a LONG ways from. If Hyundai wants to compete with the big boys they've got to nail stuff like this.