I've followed these steps but no app data restored

I've done all these steps. The apps transferred to my new phone, albeit not without a lot of angst, I believe it was due to old apps that aren't available any more. But, none of the app data transferred. No game saves, no weather stations, no other info that I've accumulated over time in each app. It's like I'm starting new. Help! Where did I fail? How to I get my data back?

And, even more importantly, how do I keep this from happening again. I need to upgrade another phone. Ugg!!