The sync has to be done from within the app itself, on your iOs device.
At the beginning of the game you should quickly see a button at the bottom of the screen saying, Already playing?
Tapping on that button will open the Options tab where you will be able to log in in your existing account.
Should you have missed that prompt, continue with the Prologue until you can access the Options tab.
There, choose the platform where you play the web version of the game and log in as usual.