Different airlines okay for 72 hour visa free transit?

Hello,
I am planning to book a flight from JFK to Harbin (final destination Harbin, with a layover in Taipei). I would like to stay in Harbin for 2 days then fly to Russia. My first flight will be on EVA Air and the second with Aeroflot. I have read conflicting reports- some websites say you can book on different airlines and others say the flights must be on an interline agreement. Has anybody done the 72 hour stay and used 2 different airlines? Any issues?
Thank you!