How do I get MIUI to allow notifications for reminder apps?
On MIUI 8, under Settings, Permissions, you can add individual apps to Autostarts.  This is the only thing that worked for apps that I wanted to keep running in the background (eg Gentle Alarm).

The permission does more than autostart an app 'cos if I don't have that permission set for Gentle Alarm and start the app manually, the app doesn't work, so I think the term 'autostart' is misleading.

The other thing you might need to do is tell MIUI to not apply any battery saving methods (depending on the MIUI version).

Having said all this, I can't get Google Now to work.  I guess I need to find the right app/module to enable in Autostarts.