Hello Kyjrod,
If your call logs are showing up on someone else's device the root cause would be that you and the other person are currently logged into the same Apple ID account on the devices. An Apple ID account should never be shared with someone else. It is highly recommended that whoever the account doesn't belong to signs out of it and into their own account on their device.
Sign out of iCloud on your iPhone, iPad, Apple TV, or Mac
Sign in with your Apple ID
With that being said, to stop the call logs from syncing you'll want to go to Settings > Phone and turn off the Calls on Other Devices option. Then go to Settings > name at the top > iCloud, and turn off the iCloud Drive option.
Cheers!