Concordia, it means that during the 24 month initial period of the written you must have been employed by an operator that has a FAA Part 121 or a Part 135 commuter certificate. And that when you take the practical exam (flight test) after the 24 month initial period of the written, you must be working for an operator that has a FAA Part 121 or Part 135 commuter certificate and have gone through their PIC training program.
This is the written opinion of the FAA legal office.
As for working for a non-US carrier is concerned, I don't believe that this will allow you to use the written after 24 months.