In order to learn how was it, I transfer first a little wordpress web with your Akeeba Kickstar Core, with no problems (I upload the backup file manually by FTP , and after I follow the instructions of your video demo)
After I tried with the Prestashop web and it dont run, because after all the process (upload backup files, database conection, and so... ) when I open the new url, it goes to the old url.
After a lot of tests and searching in Internet, I modify manually in the new database the table “ps_shop_url” and also the file “parameters.php” , and now it runs ok in the new url.
In resume : Akeeba Kickstar Core restore correctly all the folders and files, restore new database with all te data of the old-database, but do not modify the necessary files to “redirect” to the new url.
And also, after restore new database with all te data of the old-database, the file "parameters.php" contains the name and user of the old database, not the new one.
In the transfer of my wordpress web , I see a page that inform us the “replaced” strings, something like “//old url/ ...” will be //new url...”, but in the Prestashop transfer, this page is not, and then , all the data in the new database are the “old” data and “old-url”.
Sorry for my english, I wish you can understand my problem.