As I've found, many Xiaomi devices (and maybe of other companies) prevent apps from opening themselves or others, by default:
https://stackoverflow.com/questions/39366231/how-to-check-miui-autostart-permission-programmatically
http://nine-faq.9folders.com/articles/8772-how-to-manage-autostart-service-on-the-xiaomi-devices
http://en.miui.com/thread-1829332-1-1.html
https://stackoverflow.com/questions/42996646/how-to-enable-autostart-for-my-app-in-xiaomi-devices

This is very wrong, as it breaks how many apps work, by having a trigger to do something.
I've noticed that this will occur not just for background apps, but also for foreground running apps. This means that if you have notification access granted, and you close the app from the recent tasks screen, it won't get opened again (I've tried with an intent of incoming phone call in the manifest). The process will stay dead.

Please prevent breaking intents behavior and the way that app auto-start themselves or start other apps.
Do it by adding this rule into the CTS.
At the very least, such a thing shouldn't be the default behavior.

Issue 123653024