I’ve just had a go at this and it seems as if it downloads the respective live installer ISO associated with each option. I find that rather wasteful, because when I want a minimized Ubuntu Server, which is probably just the minimal task, I still have to download the whole 2.7 GiB live server installer; from Canonical’s rather strained infrastructure no less – what if we are (becoming) the DDoS attack? (some hyperbole) 
Is there no equivalent to Debian’s netinstall images? I half-expected mini.iso to be exactly that. 
I think we need a minimal image that provides a menu to select which installer program to download and run, in online mode, of course – not the whole disc image of every option imaginable. And thanks to tools like apt-cacher-ng the user can abort and restart the whole process anytime and as often as they like, without having to download at least 2.7 GiB again.