When the macOS High Sierra Installer is downloaded from the Mac AppStore, it, like any other application downloaded through the Mac AppStore, ends up in the Applications folder. The name should be "Install macOS High Sierra.app" (or its equivalent in your language).
Typical Auto-Installation Prevention
Since the first Mac AppStore-based Operating System (Mac OS X Lion) was available to download, the way to prevent an automated installation upon completing the download was to cancel (quit) the installer, open the Applications folder and move (not copy) the installer to another location such as the desktop. Having done this every time, including High Sierra (in September 2017), I can verify that it worked then too.
Why might it be beneficial?
Apple has always been known for staying top of security, rather than playing a slow game of catch-up. It's thus only natural that the latest macOS version is somewhat "forced" onto the user's computer. Afterall, for the majority of users, making the conscious decision of clicking the download button means they intend to install it right away. Unfortunately, though, there are many people who think that clicking the download button is all there is to it - that's where the application opens and a window pops up to tell them otherwise, showing them what must be done. To you and me, this is very annoying because we don't fall into the "negligent" category, but just imagine if people think they have the latest version and are up-to-date with Apple's latest technologies and security only to find out they were just half way there.
What could you try next?
I think we can both agree that if it hints at the High Sierra option at startup, it's most likely that High Sierra has been downloaded and does indeed reside somewhere on the mac.
- I would firstly suggest using Spotlight: Command +
Space Bar to make a search for "High Sierra", "Install
macOS High Sierra" or any variations of it both in English and your own language (should it be different). I have always had more success with Spotlight than the traditional Finder search bar.
Please upload an image of the prompt you get upon restarting.
Perhaps something went wrong during the download procedure and the installer is not complete as a whole, yet some part of it thinks it is (perhaps a property file was written to too early), making it seem as though the update is ready to install when in fact isn't.
For this, I would first like you to navigate to the App Store folder at
/Users/<USERNAME>/Library/Application Support/AppStore and check that directory (including subfolders) for anything that may be High Sierra related. You may wish to consider this article to resolve download issues. It may seem a little far fetched but worth a go if all else fails.
Check under the Purchases tab in the Mac App Store, that High Sierra actually appears. Are you sure you downloaded it, or are you simply getting notifications that the upgrade is available (as your comment may hint at)?
Let me know how you make out and I'd be more than happy to assist further.