Hiding behind subdirectory, but then it comes up.

So I have learn a ton doing this. Followed the steps carefully to “protect” my site by installing it into a subdirectory. I have then “copied” the .htaccess and index.php files. and modified the index.php file and placed it in the root. It looks to be correct,…

To test the security of the subdirectory reroute I enter domain.com/wp-admin. And if correct it should not go to the dashboard.

In my case, it inserts the subdirectory for me and defeats the purpose.
(ie. domain.com/subdirectory/wp-admin)

Where should I be looking for what appears to be an incorrect entry or error?

Thank you
buddie77