September 2015
Nope. I have the "Push Notifications" turned off and in the middle of my office I hear "Visitors. I better put on my pants." I am glad that it is not my boss saying that, but I am also bothered that my phone says it.
January 2016
I have android 5.0.1 and I tried turning off notifications in the app, but that did not work. I also have the show notifications box cleared that is located in the app manager details for Tapped Out (below the force stop and uninstall buttons).
I found a setting in the phone that blocks all notifications for the app and that finally worked.
settings>>sound and notifications>>application notifications>>tapped out>> Block turned to on
that has worked so far.