Question about 144 hour visa free program

Hello,

We are in the US and are planning to purchase a round-trip ticket DC-Incheon-Shanghai. We'll go first to Incheon and spend a couple weeks in Korea. Then go to Shanghai under the 144 hour free program. Leaving Shanghai we'll return directly to the U.S. but change planes in Incheon. Since the U.S. is our final destination of the last leg of our trip, would they consider our itinerary to be Incheon-Shanghai-DC or Incheon-Shanghai-Incheon (since the Shanghai-Incheon flight is direct). Another words, does this itinerary allow us to use the 144 hour visa-free program? Thank you!