In the case of PDF files and other files that can be displayed in Safari, they will not download. Or they do, they just download and display in Safari. To save them use the Share Sheet and chose Save to Files.
In the case of files that Safari can not display, like docx, then you will be asked if you want to download them. Once they download there will be a download icon, a circle with a down arrow, next to the share sheet icon. Tapping the download icon will show all files you've downloaded that session. Tapping on the file will attempt to open it in a compatible app. Swiping it will let you delete the file.
Or you can go to the Download directory in the Files app. It should show up under Favorites, or in the iCloud Drive folder. That's by default. You can change the destination of downloads in Settings > Safari > Downloads.
If Safari is opening a tab and showing garbage, it is probably because there is something wrong with the file that makes Safari thing it is a displayable file, but the file is either corrupted or has the wrong extension.
At least this is how it works on all other sites I've tried. Like I said before, I can't open Google Drive in Safari, because it always redirects me to the app.