Giving the simplest answer first: I would suggest checking if the div exists after a second (time depending on many factors - I'm sure you understand the time specifics for your site). When adding a new element (such as your twitter widget) it's important to understand that each element (in your case, "a widget") comes with certain specifications which can have major differences compared to similar (on the surface similar) "widgets"
For a short answer: "It depends on the third party widget"
For the medium answer: "If you can look at how the widget is created, you can probably find a way to 'talk to it'"
For the longer answer: "It's actually not very difficult to create something to communicate with Twitter, so if that's what you want to learn I would suggest being more specific."
Hope SOMETHING OF THIS HELPS...
edit: Knowing nothing about the widget, I would probably set an interval to make requests from client to server, either by using javascript:setInterval() or setTimeout()... If I had time/resources, I would prefer a solution where you understand both Twitter and the widget though (saves time in the future if you want to think about what you've done)...