"Allow apps downloaded from anywhere" does not prevent the popup, the setting simply allows you to open and use the app. The popup is only a reminder...
And, that message only pops up the first time you open a downloaded app, and not after you use that app a second time.
I suspect that you are not copying the app to your drive, but running the app from the mounted .dmg each time.
If you copy the actual app to your drive (you can put it anywhere), then you won't see that "first time" popup again for that app.