QSystemTrayIcon's window does not send QHelpEvent of type QEvent::ToolTip to QSystemTrayIcon object class.

QSystemTrayIcon's window should send QEvent::ToolTip to QSystemTrayIcon main class. I even know what you need to change:

bool QSystemTrayIconSys::event(QEvent *e)
{
    switch (e->type()) {
+   case QEvent::Tooltip:
#ifndef QT_NO_WHEELEVENT
    case QEvent::Wheel:
-        return QApplication::sendEvent(q, e);
#endif
+     return QApplication::sendEvent(q, e);
    default:
        break;
    }
    return QWidget::event(e);
}

It works on qt4 and it is because your help page contains the words below:

Only on X11, when a tooltip is requested, the QSystemTrayIcon receives a QHelpEvent of type QEvent::ToolTip.

then it should work on qt5 also.