An application that is not a launcher cannot capture the home button. For both screen off and pressing the home button, the app lifecycle will be the same, so it's not possible to detect that the home button was pressed.
It's not quite clear from your question, but if you want to show a different screen or "reset" the screen when the user returns to the app after pressing home, then you should probably set the noHistory flag.
This makes sure your activity is finished when the user navigates away from it, which is exactly what happens if you press the home button.
I wouldn't recommend using this flag just to show the welcome screen again when the user presses home and comes back later though. The reason is that pressing home doesn't mean a user is "done" with the app, just that something came up and switched out of your app for some reason. In that case the default Android behaviour is to return to the point where the user left when the application icon is pressed again in the launcher.
In contrast, 'exiting the app' in Android would mean that all the tasks for the app have been finished, e.g. pressing the back key for example. In that case there's nothing to return to the next time the app is launched, and the welcome activity is shown again.
I recommend you read up on the Activity lifecycle and how tasks and backstacks work in Android.