revalidateTag/revalidatePath in sever actions updates the UI without visiting the page, why?

revalidateTag/revalidatePath “only invalidates the cache when the path is next visited in Next.js” (https://nextjs.org/docs/app/api-reference/functions/revalidatePath), and they work fine inside server actions for data revalidation and UI update when the page is navigated to. The bit I do not follow is why they also working producing a desired outcome of revalidating and updating UI when we are performing data mutation (like adding product) on the page that displays data, meaning that we are not navigating to a new page after performing a mutation yet apparently cache on the page we are currently on gets purged, data gets revalidated and UI updated. One answer to that is that “Server Actions integrate with the Next.js caching and revalidation architecture. When an action is invoked, Next.js can return both the updated UI and new data in a single server roundtrip.” (https://nextjs.org/docs/app/building-your-application/data-fetching/server-actions-and-mutations), and yes it does make sense only how does the next.js knows which ‘updated UI’ is supposed to send back? updated UI in terms of server component means some form of html that is ready to be displayed, and we can have many pages that are displaying data that our revalidateTag/revalidatePath is revalidating, one server actions can be imported to many different components and yet er get the specific html update relevant for our page without navigating to that page? To reiterate my problem is that I understand the when we navigate to new page then we can get the updated UI, but when we are already on the page and display data on it and perform mutation on it (given that we can be displaying the same data on many pages) how do we get the updated UI in the server action return trip for our desired page?