In Safari 7 there is a new security setting called Safe/Unsafe mode relating to the Java plugin that the multiple file uploader component runs in. This new setting allows the Java plugin to work in Unsafe mode either for individual websites or for all sites.
In Unsafe mode the applet will have unrestricted access to local file system. It appears that this security setting works on top of Java's own security settings (restricted/unrestricted access). This setting is available through Safari preferences / Security tab / Internet plugins: manage website settings (then select Java plugin). In order for the multiple file uploader to work and gain access to your file system for uploading files, you'll need to select Java to run in UNSAFE mode for the Huddle website.
This should then allow you to start uploading multiple files on OSX 10.9, again, however if you have any additional issues then please get in touch with email@example.com or raise a ticket with us directly.