You might find that the People app in Android does not sync the contacts you added in Gmail as soon as you do it. This might be because you turned off automatic sync for your Google account in Android.
In your Android device, go to Settings -> Accounts -> Google. You can turn on automatic sync here, if you want. Else, tap on the Google login name and then tap on the Contacts option to just sync only that. Your Gmail contacts and the People contacts in Android should get synced now.
Tried with: Android 4.4.4 and Moto G