In Apache, if you have a VirtualHost, you can specify whatever DocumentRoot you want. On the same host, you can have multiple VirtualHosts all with different DocumentRoot values.
In Nginx, the document root isn't dependent on directory. Like I mentioned, https://10.10.22.35/host_ui/ is not a directory, it's a URL. The Nginx location block responds to the URL. In the block that traps https://10.10.22.35/host_ui/ I then decide what the document root should be for requests that match that URI, just like you can in Apache. In Nginx, I don't have to specify a document root in a location block, it can be global to the server but the point is, it doesn't have to be, just like it doesn't have to be in Apache.
As far as Phalcon is concerned, the index.php is invoked by the rewrite in the appropriate document root of /mae/www/html/host_ui/public/index.php and Phalcon should be obvlivious to this fact. I'm starting to think that Phalcon might be getting confused by the underscore in the directory name.
Can any of the Phalcon authors comment on this?