did you try adding the permissions when creating the page where you are adding this portlet, for the page/portlet visible to every one you need to set the "Access Permission to Everyone" so that every one can view it and its will also be available in both portal/public and porta/private spaces.
Hope this helps, let me know if you need any further clarification on the same.
you could try to set the portlet's Access Permission to *:/platform/guests that it only appears on non-authenticated mode
That's it Trong. Thanks so much!