hi ckuan, this is helpful and you seem to be coming close to understanding my issue.
I am most likely in this scenario: "If you’re using upgraded iCloud notes, you see them on iCloud.com and your devices with iOS 9 or later and OS X v10.11 or later that use the same iCloud account. If you also have devices with earlier versions of iOS or OS X, you don’t see your upgraded iCloud notes on those devices."
My response: I am using upgraded iCloud notes for both my iPad and iPhone devices both running on iOS 10.0.2 and my most current notes content mirror that of the web-based iCloud.
Question: So how then do i go about pulling/syncing these content onto my Macbook Notes (version 3.3, 2011-2014) which runs on Mac System Version: OS X 10.10.5 (14F1912)?