[Question] enable push and/or sync data

[crusades]

hello at all,
I have a question because when my innos is connected to wifi or mobile internet I do not receive any notification, but after unlock they are synced.

I have flagged gmail like "keep runnging after screen is turned off", but often gmail do not sync data, seem like phone will be freezed, and only after 2-3min they are synced.

In my past phone (jiayu g4s) all apps where synced every time, and also with phone locked.

Does I need to install one app to sync data?

Regards at all