Does examption apply for NY to Taipei, layover, Taipei to Shanghai, visit, then Shanghai to Taipe?

I noticed that one of the condition is that the exit flight has to be a third country/region. My stop in Taipei is just to change flight (4-5 hrs max), does that still mean Taipei would be where I am flying from (even though I am really travelling from New York)? What about if I book the flight as NY -> Taipei (layover) -> Shanghai -> Hong Kong (layover) -> Taipei?

Thanks!