Why doesn't my Mac recognize my iCloud password change?

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iMore Question

Why doesn't my Mac recognize my iCloud password change

My Mac is setup to use my iCloud password for login. I have changed my iCloud password, however my Mac did not recognize the change. I can login to the Mac, but only with the old password. It seems like the Mac should recognize the change, but Apple support advised that it does not, and that I should change the setting to "Use Separate Password" (See chat transcript snippet below).

Is this the case, that it doesn't sync iCloud password changes, or is it a bug. Seems like a bug to me. Any help would be appreciated!

Chat transcript:
...
B Navigate to system preferences. Users and groups. Locate your user name on the left column. Unlock the bottom left lock and then change the password.
Me: Ok. i am there. It says ?xxxxxx is using an iCloud password to log in and unlock the screen.
Me: and gives me the option to change my icloud password.
Me: but i have already changed my icloud password.
Me: and i can login to icloud on the web, and my iphone recognizes the new icloud password
B What are the other options?
Me :however the mac login does not recognize the new password
Me: Use Separate Password, Cancel
B Choose use separate password.
B Then type in the password you would like to use.
Me: Well i figured that would work, but that really doesn't solve the problem.
B There is no way for when you change the password to your Apple ID for it to auto update on the mac.
B So you can choose to use separate password and enter the one you use or enter a different one. It will not matter. If you change the Apple Id password it will not update on the mac. You will have to manually change it.
Me: Ok. The way it is worded it sounds like it would. Thanks for clarifying.