I've managed to flash TWRP to my device with this tool. Now the system update is downloading. But still it is a bug to be considered. This thread can be closed i believe.
I have the same issue on Mi Note 3, has been around since Xiaomi.eu MIUI 9 and applies to 10 as well, all stable releases. When i go to the update screen it notifies me that an update is available. When i hit download, it just pops up a message that i am already up to date and does nothing.
Second issue is that when i download the updated rom manually and restart to TWRP, the installer complains about the device name and doesn't install. My device is required to return "jason" while it returns empty string. I managed to install MIUI 10 only after modifying the install script to ommit that line.