Unfortunately the copy to Web Project action isn't very useful in practice, since it doesn't support such basic requirements as selecting which sandbox (specific user sandbox, current user's sandbox (if any), staging sandbox, etc.) the content gets copied to, nor does it allow selection of the destination folder within a Web Project (or better yet configuration of target folder mapping rules - a common requirement).
The good news is that it wouldn't take much to implement a more sophisticated version of this action - the underlying cross repository copy service (which this action leverages) does support all of these things.
Cheers,
Peter