Normally drush makes default behaviour is to create the site in the current directory - relative to where you run the command.
But the simplest way to deal with this is just to run drush-make with a parameter explicitly stating where to deploy the site:
drush make my.make relative/path/to/my/public_html
drush make my.make /absolute/path/to/my/public_html
Obviously replacing the path in question with the appropriate one. Don't understand UNIX file paths? Read up on them on wiki page.
And while I am at it, why don't you take a look at the drush make documentation too.
There are a number of drush configuration files that affect the working directory for drush commands - the most likely candidate being a drushrc file is example.drushrc.php.