I'm pretty sure I know what the problem here is; you're probably trying to turn off the console by holding down the POWER button on the GamePad. Most homebrew won't respond to the "power off" signal normally sent by the POWER button on either the GamePad or the console, but holding the POWER button down for longer will force that thing to turn off without the signal.
So why do you see the Nintendo logo and the Quick Start menu? That's because both of those things aren't streamed by the console - they're entirely stored within the GamePad firmware itself. You can prove this very easily - unplug the console from the wall, then turn the GamePad on. You'll find that the Quick Start menu still shows up. (You may need to turn the console on first - and then obviously off again - before you unplug it if it's been a while since you last turned it on, since the menu might otherwise complain that it hasn't been connected to the console for some time.) This proves that it's not the console that shows you these things, but the GamePad itself. Normally, the console turns on while the GamePad is showing the Quick Start menu. When you select a game to run, the GamePad sends a signal to the console to tell it to run that software.
(Side note: You'll also find that the TV Remote feature also works when the console is unplugged. Once again, that's code contained within the GamePad firmware, not anything enabled by the console.)
So I believe what happened in this case is quite simple - because homebrew does not respond to the "power off" signal, the only thing you turned off using the GamePad's POWER button was the GamePad itself. You'll find that the console is still running. To actually turn the console itself off in your example homebrew you need to hold down the POWER button on the *console*, not the GamePad.