Hello Lowlow_,
From your post it appears you want to be able to block a contact on one device, but not on another. The article you came from, Block phone numbers, contacts, and emails on your iPhone, iPad, or iPod touch, explains how to block a contact.
If you have iCloud for Contacts enabled, anything you do on one device, such as block a contact, is going to sync with other devices signed in with the same Apple ID that have iCloud for Contacts enabled.
You could disable iCloud for Contacts on one of the devices so it would not effect the other. Keep in mind that doing this would prevent any further syncing of Contacts between the devices.
You can find additional information regarding iCloud for Contacts, and how it works, here: Set up iCloud for Contacts on all your devices - Apple Support
Have a good day.