Find out who updated Drupal modules
I think you'll find details in the Watchdog if the updates were performed using the UI.

If the modules were updated using a different method, e.g. Drush or manually, then you'll need to turn to your server logs, assuming that you keep logs for such actions. Drupal won't hold any data about those actions, as it wouldn't even necessarily know they had occurred.

Just to clear things up, the "Recent log messages" report gets its data from the watchdog table, so you're looking in the same place for both.