i just had this problem too.
problem is that uploads are saving the full URL (with domain) to the database -- you can see this in DB table
SELECT * FROM xxx.wp_options WHERE option_name LIKE '%wp_cycle%';
this occurs in file \wp-content\plugins\wp-cycle\wp-cycle.php, method wp_cycle_handle_upload -- where it sets
i had some success changing it to:
$upload_dir_url = wp_upload_dir(); //str_replace(basename($file), '', $url);
$upload_dir_url = str_replace( get_bloginfo('url'), '', $upload_dir_url['url'] ) . '/';
you could also just perform a replace in the database field, since it's a serialized array.
UPDATE meant to use ['url'], not ['baseurl'] -- need the folder dates too, per wp_upload_dir() reference