I gave this a try to see if it's broken for everyone.
Like others, when I launched the app on my phone -- I've been playing only on my iPad so far -- I didn't see the login buttons on the settings menu that I usually see. I played along with the tutorial for a few minutes, and as soon as I got to through the tutorial (once I'm told to build more houses, so when you build the third house), the login links appeared. It only took a couple of minutes to get to that step.
I'd prefer to be asked whether I want to sync or start a new game when I first launch the app, but I hope it's helpful to other players to know they *can* sync between devices if they play through the tutorial on each device.
One little glitch to mention: If you hop between devices quickly, it may complain. I had the game open on my iPad when I finally got logged in on my iPhone. I closed the iPhone as soon as I saw that it did sync correctly, and kept playing on the iPad. A couple minutes later, I got a message on my iPad that told me I'd been active on another device and couldn't play on both at the same time. It made me close the app and reopen it to keep playing.