Hello,
The only way one site could change the details of the other is if they are both pointing to the same database, which is controlled in the configuration.php file. I can't think of any other way for that to happen. I would suggest contacting your hosting provider on this as well.
I agree, I have done this plenty of times with other sites without any issues and I know that the config file is correct with the new database. I will contact the hosting and see if we can figure it out.
Thanks for the support.