Tags are a way to help spread the microblog or thread type into the fediverse and searchable as well. While on mastodon, I can see a microblog or thread post type of article, link, etc, it'll show the tags, but the posts do not appear in the same tagged way a post from mastodon with a tag does. I think this is a bug for now.
If you are on a Mastodon instance and follow a kbin.social user for example, you will see their posts and comments to on kbin and can interact still on the same thread in kbin for example.