Asking the airline is good advice. Getting the answer in writing would be a very good idea.

You can also ask Korean authorities in writing or ask ICN airport via their website. Anything to show in writing to the airline.

Transit status has nothing to do with one or two tickets. It is related to passing passport control and entering the country, or not entering the country and staying in transit. If you stay in the transit area under 24 hours at ICN Airport you do not require a visa. The airline may not deny you boarding if you can prove this. In turn, the airline might have tonprove to authorities that they checked rules are adhered or be responsible for your costs if you try to enter the country anyway.

This information is published on the ICN airport website, Asiana and Korean Air websites and Traveldocs for example.

If you cannot show your onward ticket to prove to the first airline you will be in transit, then they woukd deny you boarding. You have to show then the onward ticket and it would, in my opinion, be just fine.

Same in Zurich, with an onward ticket from schengen to non schengen transit in two tickets is possible.

The risk is with airline staff denying boarding anyway, both check in and document check, who are often not very flexible or well trained when it comes to special situations.