andrew,
Maybe you can help me. My wife and I both have an iPhone 6 running iOS 9. She is logged in using her Apple ID and on my phone I am using my Apple ID. I added my Apple ID under her iCloud account and activated notes. When we were running iOS 8 our notes would sync between our two phones. Now with iOS 9 for some reason our notes app don't sync. It's really weird that she has the new notes app but when she taps on my iCloud account in her notes app the notes look like they did in iOS 8 and they don't sync.
Another thing to note is I have calndar activated under my Apple ID and our calendar's sync, but why not notes? Really strange.
Would you happen to know the cause of this? My iPad was updated to iOS 9 and it syncs with my phone. The only difference is is that my iPad has my iCloud signed in as the main account. On my wife's phone my iCloud ID is a secondary account, but it worked fine on iOS 8.
I really hope they didn't change something since we use the Notes app a lot and don't want to lose it.
Thanks,
Jeremy