Hello joem,
the plugin Search Generic is only for searching in differents fields, but not in differents content type.
The search in differents content type is due to the CCK field. You must fill the live value with all content types separate by comma, and set the match to "Any word exact" and specify the separate option = , (comma).
Now, for the search generique, in it's configuration, you have to add all fields in which you want to search. For the match, let the match "Permissive"
To see the query, in the search type, in tab configuration set ON the debug option.
regards.
Lionel