It's simply a matter of understanding how software updates on the system.
- Packages (software) are managed by Apt. Tools like Software Updater, Synaptic and Software Boutique manage this.
- Very, very few programs have their own way of updating themselves (like Telegram, Steam)
- Updates for software come through repositories.
- The "Upgrade" button for LibreOffice in Boutique adds the official PPA, which have newer packages, compared to the stable, well tested version by default (Ubuntu repository).
To update your software, you simply use Software Updater, or from the terminal:
sudo apt full-upgrade
For automatic updates, there isn't an option by default to turn this on for all updates (I believe security updates can be automatically installed in Software & Updates). There are workarounds someone may be able to help you with.
There are some cons to updating without user intervention, like sacrificing stability in the unlikely event an update caused problems.