Back up all data.
If applicable, sign out of iCloud in the iCloud preference pane. Leave the preference pane open.
Triple-click anywhere in the line below on this page to select it:
~/Library/Application Support/NotificationCenter
Right-click or control-click the highlighted line and select
Services ▹ Reveal
from the contextual menu.* A folder should open with an item selected. Move the selected item to the Desktop, leaving the window open. Log out and log back in.
Sign back in to iCloud, if you signed out. Test. If there's no change, or if the notifications you expect to see are not shown, sign out of iCloud again and put the folder you moved back where it was, overwriting the one that may have been created in its place. Log out and in again. Otherwise, delete the folder you moved.
*If you don't see the contextual menu item, copy the selected text to the Clipboard (command-C). In the Finder, select
Go ▹ Go to Folder...
from the menu bar, paste into the box that opens (command-V). You won't see what you pasted because a line break is included. Press return.