If you have configured the refresh cronjob as explained in the online documentation (http://docs.getasa2.com/cronjobs_repo_refresh.html) but you do not get any results, this might have something to do with the PHP command used to execute the script. By default, ASA2 uses the "php" command to execute server-side scripts. On some servers this might be an older PHP version and will not work as expected. A solution might be, to use the "php5" command.
Please try this:
Create a new shell script in your user directory, e.g. /home/[your-username]/cronjobs/asa2_repo_refresh.sh
Insert the following lines in this file, where [path-to-your-website] must be replaced with the path to your WordPress installation starting with "/home", like "/home/timo/asa2demo":
php5 -f [path-to-your-website]/wp-content/plugins/amazon-simple-affiliate/lib/IfwAsa2/Wp/Plugin/Cli/Executables/script.php -- "[path-to-your-website]/wp-content/plugins/amazon-simple-affiliate" Asa2_Module_Repo_Cron_Refresh -lt=600 -limit=10 --verbose
Then configure this script in your cPanel cronjob panel as shown on the following screenshot: