Hi David,
That’s a great question!
By design, rather than fetching the entire page, we just grab the contents of the #tribe-events-content div. There are a few ways you might workaround this.
The important thing of course is that you communicate the desired title in the ajax responses. You could do this by additionally including the events title in a hidden element, or as a data attribute for an existing element. Alternatively, you could include it in the response data by utilizing the tribe_events_ajax_response filter hook.
Client/browser-side, some Javascript could be setup to listen for successful ajax responses (the ajax-success.tribe event will be triggered) which can then grab that fresh title and use it to overwrite the content of your desired title element.
Does that make sense? Unfortunately we cannot go into too much detail with custom dev questions like this one, but I hope that at least gives you a strategy you can explore further 🙂