Notes created via Siri don't sync with Gmail until they're manually edited
I'm having the same problem on my iPhone 6 S. Like you, if I edit the Siri-created notes, they sync. In addition Siri won't create iCloud notes on that device (which is why I have reverted to Google notes.)

My work-around is to move all the notes to iCloud, which I then process on my Mac. That way, they keep the same time stamp, and I can do this in bulk on my iPhone 6 S (Notes.app) using Edit → Move All. Obviously not helpful if your other devices don't use iCloud.

my old iPhone 5, which I've kept, has none of these problems. Yet both my phones use the same OS (9.1). I'm considering keeping the old phone for Siri note-taking purposes until this gets sorted out, as I rely heavily on this feature. 

I've logged a bug with Apple Bug Reporter.