HERES A WORKAROUND - by no means ideal or what should happen, but it'll get your notes from your computer to your phone...just not in the Notes app.
I have an iPhone 6S, and I am running Yosemite still on my MacBook Pro, haven't upgraded to El Capitan, with the same problem. All notes on my iPhone sync to iCloud online, but there seems to be no communication between my Mac and iCloud online and also not to my phone. Some things I noticed that others might be able to use to solve this:
1) When I enabled Notes (not Mail) in iCloud on my Mac, it forced me to create an icloud email address. My AppleID is not an icloud email address, but now I also have this new iCloud email address.
2) In digging around with this, and noting (sorry) the way the Gmail does it, I found that my icloud.com email address automatically creates an invisible folder called - you guess it - Notes, where it stores the notes created on my Mac. I can access that folder (with the notes created on my Mac) in Mail on my iPhone if I set up the iCloud email account there - BUT ONLY IF NOTES IN THE ICLOUD SETTINGS IS TURNED OFF ON MY PHONE, BUT TURNED ON ON MY COMPUTER. If I turn Notes on on my phone, the folder becomes invisible again, and I can't access anything except on my computer.
3) This suggests to me that when Notes is turned on, the icloud.com email address assigns that Notes folder to the Notes app...but there is some sync issue there, and I think Apple is the one that needs to fix that...unless someone has some other ideas.
In the short term, I'll leave iCloud Notes on my phone OFF, while iCloud Notes on my computer are ON, and I'll access them through the icloud.com email address. A hassle, but the only workaround I've found...