As you probably found out by searching this MIUI (Chinese versions specially) has a few problems with notifications coming out late or only after unlocking the device. This issue is due the agressive battery saving policy that Xiaomi does on their software.
Luckily there’s some workarounds without having to flash another ROM like xiaomi.eu or any other AOSP based ROM.
So let’s try to fix your Notifications:
1. Long press the icon of the App you want to fix >App Info
– Enable “Autostart” and change Battery Saver > “No Restrictions“;
– Enable Notifications, Notifications on lockscreen, etc.
2. Go to Settings > Wifi > WLAN Assistant
– Enable the “Stay connected” option and the “Traffic Mode”.
3. Go to Settings > Security > Security > Settings (top right corner);
– Go to Boost Speed and enter Lock Apps. From this tab, lock the apps you want notifications to receive from and Clear cache when device is locked section to “Never”.
4. Go to Settings > Battery > Settings (top right corner).
– Set the first two options under “Lock Screen Settings” to “Never”;
– Enter the Application Battery Saver section. Disable the apps that you want to enable notifications from;
– Enter “Scenarios” and disable sleep mode.
5. Go to Settings > Privacy > Protection > Special Permissions.
– Set “Adaptive notifications” to “Android”;
– Enable the apps that you want to enable notifications from “Restricted data”;
– Disable the apps that you want to enable notifications from “Battery optimization”;
– Make sure that the ‘Notification Access‘ option is set as ‘Enable all‘;
– Enable the apps that you want to enable notifications from the “Do not disturb settings”.
6. Go to “Security > Game Turbo > Settings” (top right corner).
– Turn off the Game Turbo feature.
With all of these changes or at least some of them you should have your Notifications coming instantly as it should be. Feel free to test and share your feedback on the comment section.