Just make sure that the last thing you see is a loading screen with "synchronising", and you should be fine. You can trigger that either by going to KL or by going to the neighbours screen and back. After seeing that, don't do any more tapping, just exit the game. You should then be able to use your other device without seeing the warning.
Another way to do it: if you do see the warning and still have your original device handy, leave the warning up and then start the game on your original device. It should immediately synchronise and will then show a popup saying it's now safe to use the other device, and will then stop at the login screen. At that point tap Home or something to exit without logging in, and then you can tap OK on the second device and log in.