Up to parent activity - on Android

You need to set up the PendingIntent which is used to build Notification, to start a fresh task, and provide the PendingIntent with a back stack to achieve the application's normal Up behavior.

Intent resultIntent = new Intent(this, SecondActivity.class);

TaskStackBuilder stackBuilder = TaskStackBuilder.create(this);
// All the parents of SecondActivity will be added to task stack.
stackBuilder.addParentStack(SecondActivity.class);
// Add a SecondActivity intent to the task stack.
stackBuilder.addNextIntent(resultIntent);

// Obtain a PendingIntent for launching the task constructed by this builder.
PendingIntent pendingIntent = stackBuilder.getPendingIntent(REQUEST_CODE, PendingIntent.FLAG_UPDATE_CURRENT);

NotificationManager manager = (NotificationManager) this.getSystemService(NOTIFICATION_SERVICE);
Notification notification = new Notification.Builder(this)
    .setContentTitle("My Notification")
    .setContentText("Notification content")
    .setSmallIcon(android.R.drawable.ic_menu_view)
    .setContentIntent(pendingIntent)
    .build();

manager.notify(NOTIFICATION_ID, notification);

Please read the Android official documentation on Preserving Navigation when Starting an Activity. It recommends the above approach.

I use the following code and it works like a charm. Have a go!

Intent upIntent = new Intent(getApplicationContext(), Home.class);
if (NavUtils.shouldUpRecreateTask(this, upIntent)) {
    Log.d("ShowNotifications", "New Home");
    TaskStackBuilder.create(this).addNextIntentWithParentStack(upIntent).startActivities();
} else {
    Log.d("ShowNotifications", "Old Home");
    upIntent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP|Intent.FLAG_ACTIVITY_SINGLE_TOP);
    //upIntent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK | Intent.FLAG_ACTIVITY_CLEAR_TASK );
    startActivity(upIntent);
    finish();
}