I guess this just boils down to what auto-layout addresses: a layout can look perfectly fine on one device and not another. Or, perhaps, vice versa.
Make sure you follow instructions: Do this tutorial with the simulator set to iPhone 6. Otherwise, you might be left like me, wondering why my intermediate results look just fine while the example in the book needs work. (Hint: you have a lot more space to work with on an iPhone 6s Plus!)
I feel kind of dumb posting this, but just in case anyone else runs into this issue, maybe this will help.