iControlWP does not automatically upgrade WordPress core of themes by default. It will never automatically upgrade any asset on your site, unless it is configured to do so.
We currently only offer the option to automatically upgrade individual plugins. iControlWP will only perform automatic upgrade for the plugins that you've configured to do so.
However, iControlWP will not perform any automatic updates on WordPress core of themes.
Why do we not auto-update WordPress core or themes?
This comes after a long process of assessing risk and customer preferences. Automatically upgrading themes is a direct route to disaster, so we've never offered this, and automatic WordPress core upgrades aren't advisable either, except perhaps for minor upgrades - which WordPress is configured to perform anyway.
We also suggest you to read: