Ok so I changed the setting of the website (example.com) in the test virtual server (Debian ISPConfig 3) to ModPHP and it works as expected.
However my currently running website http://www.swartsit.com
is running under Fast-CGI
NOOB ALERT: I don't know the differences at all
But I use these "addons" to my client0:
phpBB3 = Forum
WordPress = Blog
So is this the right direction or am I completely mistaken?