Jerome thank you for your answer...
The above screenshots are from our website.
Now take a look at the screenshots from your DEMO website:
1. Logged in to your demo website went to the Vendor Control Panel and created a shipping method
2. After we have created a shipping method, we move to the products page to create a new product.
3. In the same page if we click on "Apply" the Shipping appears!
Now that we have screenshots of your DEMO site too, please tell us how we can set your component to show "Shipping Prices" without having to click on "Apply" first.