Getting my data back

So, I've had this issue for a while, but forgot about it, then uninstalled the game. I was watching the S5 premiere, and I thought "What the hell. I'll redownload it again." So I completed the tutorial, and I encountered the exact same issue as before when trying to get my data back. Whenever I tap on the green controller icon to get to where I saved my data, my phone starts to go to another application/window, but instantly cancels the action, and I'm on the title screen like I never clicked it in the first place! It's an issue that I can't overlook, because I like to make sure my data is secure, and when I inevitably get a newer phone, when this one dies on me, I'll need to transfer my data if I'm still playing/come back to the game. If anyone could help, that'd be greatly appreciated. (I've attached the best example I could screenshot for what happens when I click on the button. As I said before, it then cancels the action and acts like nothing happened.)