Shared Hosting Directory Structure

I recently switched from one shared hosting company to another. Both plans included WHM and Cpanel. After gaining access to the new WHM, I created a second domain (the first was established by the hosting company upon startup with a domain name I had just purchased). At that point, both domains showed in WHM; I could access both with Cpanel, and I could properly use SFTP to access the correct /home remote starting directory for each of the two domains.

I had provided my new host with a full Cpanel backup of the second domain (the one I just installed on my new account myself) from my old host. That night the new host restored all files including mysql.

At this point, I can still access the original domain (established by my new host the previous day) just as I did before. However, now I cannot access the restored domain using SFTP ("can't find directory" error message). I have to use FTP. Also, I can't acccess the proper starting directory. My FTP agents (I've used two) go immediately to /public_html, nor can I go up even one level. This means that I've lost the ability to access two higher directory levels in the ususal /home/mydomain/public_html directory structure.

I've used various starting remote directories within my third party FTP agents to no avail.

Support is courteous, but stumped. They indicate that the directory structure looks fine from its end. Indeed, if I use Cpanel file management for the problematic domain, I too can see and access /home/mydomain-name, something I can't do using third party agents.

I am concerned that security may be problematic with this situation. Even though I can access the suspect domain using Cpanel and see its front end with a browser, I wonder whether there might be issues down the road.