72-hr visa free Hong Kong to Chengdu R/T?

Hello, my family (with US passports) will be traveling from ICN (Seoul, Korea) to HKG, then departing HKG to CTU on the same day. We will staying at Chengdu for 3 days then returning to Hong Kong, with final destination back to USA. Hong Kong to chengdu flight is a separate plane ticket purchase. Do we qualify for the 72 hour free transit, or do we need to apply for it? Please reply. Thank you very much.