Responsive jcarousel doesn't resize images
I think JCarousel still uses 0.2.x version of the JCarousel library and the example you're refering uses version 0.3.3 of the library which brings wider responsive support. Since 0.2.x and 0.3.x are not compatible as one can read here https://github.com/jsor/jcarousel, I think it will be difficult to achieve the features of the 0.3.x library in the drupal module. Look at the roadmap on https://www.drupal.org/project/jcarousel