The Programs & Events thinks it's pulling upcoming events, but clearly it isn't. Some of those events are recurring, so I'm not sure exactly what the issue. I started digging into the code, and got as far as TribeEventsQuery::getEvents but I'm not really sure what's wrong here. Part of it, looking at the post meta, is that event recurrence is a stringified structure that couldn't be queried against under ideal circumstances, much less via WordPresses built-in get_posts type thing.
Any idea how to get this widget to accurately show the next N events in the future sorted nearest on top? (Ideally including the next instance of a recurring event, but if that isn't possible, at least not showing past events would be a good start.)