Notes from iCloud account don't sync with devices when added as secondary account
I have the same problem syncing with my wife's notes. I found an obscure note in a marginally related Apple article about this: https://support.apple.com/en-us/HT205015. At the very end, under "Learn More" it says

"If you’re signed in to more than one iCloud Mail account on your iOS device or Mac and have notes syncing turned on, you can only use the new Notes features with your primary iCloud account. You can see your primary account in Settings > iCloud, or System Preferences > iCloud."

This really sucks since there is no workaround once you've upgraded.