Issue with timer updated child component and mouseOver dependent parent background colour

Please consider the following PIP:

/*******************************************************************************
 The block below describes the properties of this PIP. A PIP is a short snippet
 of code that can be read by the Projucer and used to generate a JUCE project.

 BEGIN_JUCE_PIP_METADATA

  name:             TimedComponentPIP

  dependencies:     juce_core, juce_events, juce_graphics, juce_gui_basics
  exporters:        xcode_mac

  moduleFlags:      JUCE_STRICT_REFCOUNTEDPOINTER=1

  type:             Component
  mainClass:        ParentComponent

 END_JUCE_PIP_METADATA

*******************************************************************************/

#pragma once

#include <memory>

class TimedComponent : public Component, private Timer {
public:
  TimedComponent() { startTimer(1); }
  void timerCallback() override { repaint(); }

  void paint(Graphics &g) override {
    g.setColour(Colours::white);
    g.drawRect(getLocalBounds());
  }
  
private:
  JUCE_DECLARE_NON_COPYABLE_WITH_LEAK_DETECTOR(TimedComponent)
};

class ParentComponent : public Component {
public:
  ParentComponent() : label_(std::make_unique<Label>()),
    timedComp_(std::make_unique<TimedComponent>()) {
    label_->setText("TimedComponent Bug", dontSendNotification);
    label_->setFont(24.f);
    addAndMakeVisible(label_.get());
    addAndMakeVisible(timedComp_.get());
    addMouseListener(this, true);
    setSize(600, 400);
  }
  ~ParentComponent() {}

  void paint(Graphics &g) override {
    g.fillAll(Colours::black);
    if (isMouseOver(true)) {
      g.fillAll(Colours::grey);
    }
  }

  void mouseEnter(const MouseEvent &event) override { repaint(); }
  void mouseExit(const MouseEvent &event) override { repaint(); }

  void resized() override {
    label_->setBounds(getLocalBounds().removeFromTop(50).withTrimmedLeft(50));
    timedComp_->setBounds(getLocalBounds().reduced(50, 50));
  }

private:
  std::unique_ptr<Label> label_;
  std::unique_ptr<TimedComponent> timedComp_;

  JUCE_DECLARE_NON_COPYABLE_WITH_LEAK_DETECTOR(ParentComponent)
};

We have a Component whose Timer triggers the repaint method. The background of this component is transparent. The background of the parent component is either grey (if the mouse if over the component) or black (if it is not). Mostly this works as expected, but sometimes – if the mouse is moved in or out of the child component – the child component incorrectly shows the black background.

Any idea how to fix this? Thanks!