I'd want to get this straightened out ASAP. If KE isn't going to give you a hotel, you need to make a reservation unless you plan to sleep in the airport, if that's allowed in Korea. Check the sleeping in airports website. I was in the KE lounge briefly last week and didn't notice any comfy place to nap briefly let alone spend the night, but I wasn't looking. If KE does provide a hotel, with a full J fare and SkyTeam ElitePlus status, you should land in someplace decent.

There doesn't seem to be a transit hotel in the airport--again, I had no reason to check--but there's a nice but somewhat dated Hyatt with lounge that's a five minute drive, with shuttle service three times per hour. There are a couple other hotels very close to the airport, some in Incheon itself some distance from the airport, or you could invest the time and money to go into Seoul for the night.