sharing a folder across a network

I set up a test situation where I have two folders on a 2nd computer in my office. That computer has a local administrator account called "User." I created 2 standard users and set one folder to be shared with one user and the other to be shared with the other user.
When I connect to the 2nd computer through file explorer, it works as I want. One user can access one folder but not the other, and visa versa.
I am now trying to do the same for a client in his office but an not having the same success.
I followed the same steps in sharing but both users can read/write the others folders/files.
The only thing I can see that is different is that in the Network Access window I see an Administrator as the owner and the computer's user with Read/Write permission. When I delete the computer's user, it just comes back after I save everything.
You may be able to follow my scenario if you look at the attached screenshots. The first 2 pages are on the test computer in my office. The 3rd page is from the client's office.
I am not strong on networking so any thoughts would be gratefully appreciated.
Thanks