You can try to use the Inspect Element in Chrome/Firefox and see that the markup of site using Moodle cms is totally different, the image is included in div tag and it has class and this class is styled with transition effect – a property of CSS 3.
If you want to have same effect, you need to have class for each image and add transition effect for it. This will require much customization and take time. If you’re not familiar with code, I recommend you to hire a developer to get it done for you.
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