In the WP toolkit I have auto-update of Themes enabled. My theme has an update. Theme author has hooked it into WordPress's update function and it shows as update in WordPress and Plesk. However, it is not updating. If it shows in Plesk I'd expect it to auto-update.
Automatic updates of WordPress core, plugins and themes occured once a day by scheduled task. Could you please clarify, is your theme is marked as outdated at the card of WordPress instance at WordPress Toolkit?
Do you see an available update at the moment?
Auto update task should be running every night to apply all the available updates. Before the task was started automatically you may see that some update is available.