Since Shopify documentation never fully explains anything and whenever I ask no one answer, I have to find solutions to every Shopify problem myself (real pain). This is no exception.
To solve this, first, you deploy your app blocks and add it manually using Theme Editor. Then you go to the "Edit code" section in your Theme, go to "product.json", and scroll down til you find the App Blocks property (really easy to identify because the name of the property is a really long id).
Then to activate it automatically, copy that property, duplicate the product.json using Asset API, and also use Asset API to add that property to that duplicate file (remember to add the property's name to the block_order property as well). Finally, assign the product template to that product.json duplicate template/file.
Why do you have to duplicate the product.json file instead of just editing the file itself? Because Shopify will just reset the code for default files anyway, which is understandable but it doesn't notify you.
