Tiff is normally a smart image document that prefers to save multiple images to a single document. You must have an option that is specifically overwriting that functionality to create multiple Tiff documents instead of one single Tiff.
I would review your scanning profiles and see if you can either try a Scan to PDF option or reconfigure your current choice to scan to Tiff. Perhaps it would be easiest to simply create a brand new scanning profile from the HP software you are using.
Normally when using a profile that merges all pages into a single document the HP software will prompt the user to add additional pages or not. That option is not necessary when scanning to individual pages which would explain why you are not seeing the "Add to current file" option.