Please follow these steps if you are having difficulty enabling caller ID on your Note 4:

Device settings > Apps > Eyecon > other permission > Appear Above Lock Screen

Security -> Other Permissions -> Find Eyecon -> Display pop-up window

Security -> Permissions -> Auto start -> Enable Eyecon

Settings -> Battery & Performance -> Manage Apps -> Battery Usage -> Choose Apps -> Eyecon -> No Restrictions

See here for general Xiaomi solutions.