No. There are two solutions for this problem.
1) Enable the cgi checkbox for this website and then create a symlink with the name php in the cgi-bin directory of the website (which is in the website root, not inside the web directory as /var/www/web1/web/cgi-bin is virtually mapped to this directory) which points to php cgi binary.
2) You create a global alias for the cgi-bin directory and place the symlink for php there, so you dont have to create the symlink for every website manually.
But 2) is normally created automatically by debian, so I wonder why it does not work for you as you said that it worked as you added the addtype and action is the apache configuration directly. maybe you activated suexec in your apache which prevents access to the global cgi directory.