To answer your earlier question, you can't test it with just a single contact. In order to fix this you'll need to disconnect your contacts on your Mac from your iCloud account. When you reconnect again, only the contacts currently in iCloud will reappear on your Mac, which is why it's necessary for the iCloud contacts (on icloud.com) to be up to date.
There are a couple of other options, both of which have issues. Once is to back up your contacts on your Mac, delete the contacts from iCloud, then reimport the contacts on your Mac to icloud.com. This isn't difficult if you don't have lots of groups. Since you do, I'm not sure this option will work for you as you would have to recreate them again.
The other option is to add all the your contacts on your Mac to icloud.com, creating duplicates, then disconnect your Mac contacts from iCloud, reconnect your Mac contacts to iCloud (downloading the full list, including the duplicates), then use the Address Book Card>Look for Duplicates feature to locate and merge duplicates. This will merge contacts with the same name, which may or may not be what you want to do. This has the benefit of keeping your groups intact as they will still be on icloud.com, and would be redownloaded to your Mac when you reconnect. However, it will not retain any association the new contacts may have with your groups, as their group assignments are not in iCloud.
Of course the other option is to take the time to go through your contacts to identify which ones are new and add them on icloud.com, as suggested earlier.