I've just unpacked a new phone Moto G 2nd Gen and noticed that the Google Play My Apps is completely empty (it's for my wife, she didn't use android before).

So I updated several essential apps (chrome, gmail, maps) manually by searching them in play store manually and clicking "Update". Now they appeared in the list of apps.

But how can I ensure that all built in apps eventually update automatically as soon as they are not in the list?

It's painful to do that manually - some apps are not even in App Drawer (like Google Keyboard).

I've just unpacked a new phone Moto G 2nd Gen and noticed that the Google Play My Apps is completely empty (it's for my wife, she didn't use android before).

So I updated several essential apps (chrome, gmail, maps) manually by searching them in play store manually and clicking "Update". Now they appeared in the list of apps.

But how can I ensure that all built in apps eventually update automatically as soon as they are not in the list?

It's painful to do that manually - some apps are not even in App Drawer (like Google Keyboard).

UPDATE:

Just to let you know: all the built in apps updated automatically and appeared in the list of "my apps"

PS: to be precise only some of them updated, others just appeared there waiting for granting more permissions