solution by: https://stackoverflow.com/questions/45909147/qt-c-dynamically-style-an-individual-tab-in-qtabwidget

main.cpp

#include <QApplication>
#include <QMainWindow>
#include <QTabWidget>
#include <QTabBar>
#include <QStylePainter>
#include <QStyleOptionTab>
#include <QTimer>

class TabBarAlert : public QTabBar
{
    int indexAlert = -1;
    QColor mColor;
    Q_OBJECT
public:
    TabBarAlert(QWidget *parent = Q_NULLPTR):QTabBar(parent)
    {
        mColor = Qt::red;
    }
    void setIndexAlert(int index){
        if(indexAlert == index)
            return;
        indexAlert = index;
        update();
    }

    int getIndexAlert() const{
        return indexAlert;
    }

    QColor getColor() const{
        return mColor;
    }
    void setColor(const QColor &color){
        if(color == mColor)
            return;
        mColor = color;
        update();
    }

protected:
    void paintEvent(QPaintEvent *event){

        if(indexAlert> -1 && indexAlert < count()){
            QStylePainter painter(this);
            QStyleOptionTab opt;

            for(int i = 0;i < count();i++)
            {
                initStyleOption(&opt,i);

                if(indexAlert == i)
                    opt.palette.setColor(QPalette::Button, mColor);
                painter.drawControl(QStyle::CE_TabBarTabShape, opt);
                painter.drawControl(QStyle::CE_TabBarTabLabel,opt);
            }
        }
        else{
            QTabBar::paintEvent(event);
        }
    }

};

class TabWidgetAlert : public QTabWidget
{
    TabBarAlert *tb;
    QTimer *timer;
    bool on = false;
    int indexAlert = -1;

    Q_OBJECT
public:
    TabWidgetAlert(QWidget *parent = Q_NULLPTR):QTabWidget(parent)
    {
        tb = new TabBarAlert(this);
        setTabBar(tb);
        tb->setColor(Qt::black);

        /*
        *Disable the alert if the current tab matches the alert tab.
        */
        connect(this, &TabWidgetAlert::currentChanged, [this](int index){
            if(index == tb->getIndexAlert()){
                tb->setIndexAlert(-1);
                on = false;
                timer->stop();
           }
        });

        timer = new QTimer(this);

        /*
        *Create the blink
        */
        connect(timer, &QTimer::timeout, [this](){
            tb->setIndexAlert(on? indexAlert: -1);
            on = !on;
        });
    }

    void setAlert(int index){
        indexAlert = index;
        timer->start(100);
    }
};

#include "main.moc"

int main(int argc, char **argv)
{
    QApplication app(argc, argv);
    TabWidgetAlert tabs;
    tabs.addTab(new QWidget(),"TAB 1");
    tabs.addTab(new QWidget(),"TAB 2");
    tabs.addTab(new QWidget(),"TAB 3");

    tabs.setAlert(1);

    tabs.show();
    return app.exec();
}

TabWidgetAlert.pro

#-------------------------------------------------
#
# Project created by QtCreator 2017-08-27T16:40:21
#
#-------------------------------------------------

QT       += core gui

greaterThan(QT_MAJOR_VERSION, 4): QT += widgets

TARGET = TabWidgetAlert
TEMPLATE = app

# The following define makes your compiler emit warnings if you use
# any feature of Qt which as been marked as deprecated (the exact warnings
# depend on your compiler). Please consult the documentation of the
# deprecated API in order to know how to port your code away from it.
DEFINES += QT_DEPRECATED_WARNINGS

# You can also make your code fail to compile if you use deprecated APIs.
# In order to do so, uncomment the following line.
# You can also select to disable deprecated APIs only up to a certain version of Qt.
#DEFINES += QT_DISABLE_DEPRECATED_BEFORE=0x060000    # disables all the APIs deprecated before Qt 6.0.0


SOURCES += \
        main.cpp