i actually don't like xiaomi.eu very much.. a lot of info here really beats around the bush and/or exists in much simpler forms originally (from china). a lot is also lost in translation.
sean, "system updater" is infact the "updater app". when on that screen, click the menu button (on the phone itself) and a list of options shows up. from those options, select "select upgrade file" and choose the rom you've downloaded - assuming it's an official rom.. if you don't know where to find one, just go here http://www.miui.com/download-82.html and click the green button.
it'll reboot the phone first and proceed to update.
edit: make sure you've ticked TD or WCDMA version at the top of the chinese page first.