When does the user interface translation gets updated? If you turn off  "Check for updates" in /admin/config/regional/translate/settings, on what occasion does the user interface translation actually gets updated? 

As far as I know there're two ways to update it:


Installing modules. (Related PO files will be downloaded and imported)
Manually importing PO files from /admin/config/regional/translate/import


Is that all?
The check for updates is being called on the cron job 'Interface Translation'
If you disable the cron job or disable the "check for updates" on the page you mentioned, there will not be an automatic update on cron runs.

The other methods you name are manually methods. 

There is one more method in Core UI, if you translate the interface text manually on the admin/config/regional/translate page.

It also depends on the settings "Import behavior" on the admin/config/regional/translate/settings page. If the import gets updated.

This is what I know is available in Core UI.

You can of course have other contributed modules as Drush or Drupal Console to update your translations.
Or even Composer see https://github.com/drupal-composer/drupal-l10n