This is a common problem people run into. It isn’t due to Easy Updates Manager itself but is something on you or your hosts end.
For starters, what host provider do you use? Some hosts disable automatic WordPress updates for stupid reasons.
Have you checked your wp-config.php for anything that is disabling automatic updates? Look for something like define( 'WP_AUTO_UPDATE_CORE', true );
or something similar.
Have you tried using the “Force Updates” button in the advanced tab?
Try those and let me know if it works or not. Also remember that unless you setup a cron job it is probably going to take 24 hours for the automatic update to happen.