Why don't my icloud.com contacts download to my iPhone?

I've manually imported my Google Contacts into icloud.com (via a vCard file). Now I'd like to have these contacts available on my iPhone. My iCloud is property set up (Settings > Mail, Contacts, Calendars > iCloud). "Fetch New Data" is set to Push, "Contacts" switch is turned on.

Nevertheless the contacts don't sync. How can I analyze and fix this?