How to catch C++ signal in QML signal handler after type registration?

I think your code should work well.

I don't have the whole code so I don't know if you have the right methods implemented.

In order to get the signal using qmlRegisterType you need some requirements. Check if you have the Q_PROPERTY macro call implemented. Any property that is writable should have an associated NOTIFY signal that is emitted whenever the property value has changed.

If so, when you change the color property in the SetMessage component, the signal onColorChanged should be triggered.

Here you have an example where two signals are emitted: the first one when the size property is updated and the second one if the C++ mouseClick method is called using a MouseArea.

By the way, you don't need setContextProperty to integrate your C++ class with QML. qmlRegisterType should be enough. Or vice versa, depending on your needs. You can use both, but then you will have two different objects to work with. It really depends on what you want to achieve.

main.cpp

#include <QGuiApplication>
#include <QQmlApplicationEngine>
#include <QtQml>
#include "customitem.h"

int main(int argc, char *argv[])
{
    QGuiApplication app(argc, argv);
    qmlRegisterType<CustomItem>("CustomItem", 1,0, "CustomItem");

    QQmlApplicationEngine engine;
    engine.load(QUrl(QStringLiteral("qrc:/main.qml")));

    return app.exec();
}

customitem.h

#ifndef CUSTOMITEM_H
#define CUSTOMITEM_H

#include <QObject>

class CustomItem: public QObject
{
    Q_OBJECT

    /*
     * Any property that is writable should have an associated NOTIFY signal.
     * Ref: http://doc.qt.io/qt-5/qtqml-cppintegration-exposecppattributes.html#exposing-properties
     */

    Q_PROPERTY(int size READ size WRITE setSize NOTIFY sizeChanged)

public:
    CustomItem(QObject *parent = 0);

    int size() const;
    void setSize(int);

    Q_INVOKABLE void mouseClick();

private:
    int m_size;

signals:
    void sizeChanged(int size);
    void clicked();

public slots:
};

#endif // CUSTOMITEM_H

customitem.cpp

#include "customitem.h"
#include <QDebug>

CustomItem::CustomItem(QObject *parent)
: QObject(parent), m_size(0)
{
}

int CustomItem::size() const
{
    return m_size;
}

void CustomItem::setSize(int size)
{
    m_size = size;
    emit sizeChanged(m_size);
}

void CustomItem::mouseClick()
{
    qDebug() << "CustomItem::mouseClick()";

    emit clicked();
}

main.qml

import QtQuick 2.5
import QtQuick.Window 2.2
import CustomItem 1.0

Window {
    visible: true

    TextInput  {
        id: mySize
        x: 0
        y: 0
        text: "100"
    }

    CustomItem {
        id: customItem
        size: mySize.text

        onSizeChanged: console.log("size changed:", size)
        onClicked: console.log("onClicked!")
    }

    Rectangle {
        id: rect
        x: 50
        y: 50
        width: customItem.size
        height: customItem.size
        color: "red"

        MouseArea {
            anchors.fill: parent
            onClicked: { customItem.mouseClick() }
        }
    }
}