I never had a problem with Reminders syncing.
I just tested Notes on my iPhone 7+. I had to kill the App and relaunch it and the notes updated.
Syncing works better on my iPad Mini 5 but it is not 100%.
Syncing works on macOS High Sierra though - I have not had any problems with HS.
My belief is that the cause of this problem is the same as that for the Mail App. I have a similar problem there where email loads but the UI doesn't update. That is it doesn't show the new emails. Sometimes I have to do a bunch of pulls to see it but usually I have to kill the mail app and relaunch it and then they show up.
It's possible that it's a problem with certain types of hardware too. At any rate, my workflow is to kill the app on the iPhone and relaunch it. For stuff that doesn't sync, and it still happens sometimes, I go into macOS and retype it off the mobile device.
It's also possible that it's a server-side problem.