You don't have to worry, as long as you can present a return ticket. it can be on any other airline, but you must have a copy (physical preferred) of that e-ticket. The agent will most likely input the e-ticket into their system. These countries are very strict and will penalize the airline, if someone is denied entry into their respective countries.

I have flown one way on Peach to Osaka Kansai and Vanilla Air to Tokyo Narita, but there was never a problem, as long as I presented an e-ticket leaving Japan. I just presented an electronic copy form i-Phone. The agent typed in the e-ticket number or whatever info into the system, and there was no problem getting a boarding pass.

As a habit, I always printed out all my e-tickets and kept them in a file in my carryon. If you are planning a multiple segment trip in and around Asia, you should do the same.

Carfield