The exact behaviour of the dispatcher in this situation will depend on your configuration:
Is the dispatcher configured to use TTLs (via the `/enableTTL` setting)?
Or, is it using .stat file based invalidation with a dispatcher flush agent?
In case #1 above, the time-to-live on the content in question (often set with the ACS AEM Commons Dispatcher TTL feature) will need to expire before the page will be "refetched" from the publish tier.
In case #2, .stat files will be "touched" in the cache (to update their last modified timestamp) when the dispatcher flush request is received. The exact stat file(s) which are touched will depend on the `/statfileslevel` configuration. A value of "1" in this case should work, but may cause additional unnecessary load on the publish tier by re-rendering pages which are otherwise unrelated to the published XF.
Another approach to case #2 would be to leverage the ACS AEM Commons Dispatcher Flush Rules feature to create "smarter" flushing schemes, which could flush your HTML content at specific paths when an XF is published.