Do the inbound and outbound tickets need to be with the same airline?

Do the inbound and outbound tickets need to be with the same airline? Or can I have two "one-way" tickets as long as the tickets are in and out from two separate countries?

I want to fly from Seoul to Beijing on one airline, and two days later fly from Beijing to Christchurch on a separate airline because of the times and flights offered. Is that going to be a problem while using the 72 hour free transit? Thank You