In your website settings, advanced tab, do you have a block like this?

location / {

try_files $uri $uri/ /index.php?$args;

}

If so I have found that adding another block right before this is all that is needed

location /site {

try_files $uri $uri/ /site/index.php?$args;

}

I'm not entirely sure if there is a more elegant way to do this though.