Try handling onActivityResult:
public boolean onActivityResult(int requestCode, int resultCode, Intent data)
{
if (requestCode == RC_YOUR_UNIQUE_ID
&& resultCode == GamesActivityResultCodes.RESULT_RECONNECT_REQUIRED) {
mHelper.disconnect();
// update your logic here (show login btn, hide logout btn).
} else {
mHelper.onActivityResult(requestCode, resultCode, data);
}
return false;
}
RC_YOUR_UNIQUE_ID is id you've used for showing Leaderboard or Achievements activity.