There is no official AdSense app for phone or tablet. The only thing they've released is an extension for Chrome (and it's kind of buggy)
You can get third party apps, but ... you have to hand over your login credentials to use them, and you may or may not want to do that. If I wanted to break into a bunch of Google accounts, I can't think of a better way to try it than to release an app that captured the login credentials.
I have seen that message before, explorador. Google is just getting more vigilant in policing the security. This is not a bad thing in my opinion. If someone appears to log in to my account from East Elbonia, I want Google to verify it, even if it's me going through a proxy.
I've put all my important Google accounts (and client Google accounts) on two-step authentication. It's a PITA but it's a lot easier than it used to be, thanks to the smartphone app that gives you the verification numbers, and it's one more layer of security.