iPhone/Google contacts switched from Exchange to CardDAV but one way sync only

Having read the answers to , I switched off Contacts on the Exchange account, and set up CardDAV following Google instructions. Google is set as the default account on the iPhone. I have nearly instantaneous updates from the iPhone to Google. But I've waited a couple of hours and have yet to see a new contact and an update to an existing contact that I made via web Gmail show up on the phone. Is there a setting I'm missing? Per Google help, I already checked that the Account is on, and that I am using SSL. I'm on iOS 6.0. Well, seven hours later I have the updates on the phone. Is this the norm?