Set a Volume's permissions to group write for all files and folders
You can fix this on a folder on the drive using an Access Control List (ACL) to set the right permissions.

Check the man page for chmod(1) and you will need to set 'file_inherit' and 'directory_inherit' on the parent folder and then set permissions on it to read and write the group but nothing for all users.

You may also need to turn on the use of ACLs for SMB sharing if you are sharing via SMB rather than AppleShare.