Look for either domain parking or domain alias in DirectAdmin. You need to park the domain on your WP install/create an alias for your mapped domain that points to your WP install.
Ron, what do you mean by "DirectAdmin"? Your response here doesn't make sense to me, because I don't understand the terms you're using.
I have the same problem as described by Doubleface. Would you mind explained a little more how to set this up to work to that the mapper domain is always shown in the url, even then accessing http://www.site1.com/wp-admin (to stick the example), instead of changeing to http://www.multisite.com/site1?