How Does the Twitter API Work
Twitter is a REST based API. Which means various third parties have built applications that hit the Twitter servers via a URL. This is in the form of an HTTP Request. Imagine if every time a third party app wanted to update their information they requested everything in your timeline. That would bog down the Twitter servers and two it would mean a clumsy user interface. Hence there are some limits as to the requests you can make to Twitter including the number of requests. The point is there are limits. So essentially what that means is that if a third party creates a UI or interface such as HootSuite or TweetDeck they can’t just make unlimited requests constantly to update the application.
Why Is That Important
Bottom-line most third party apps use some sort of caching mechanism so as to limit heavy payloads of data that they’ve already requested. Which means you guessed it the third party app could actually have a cached view of your timeline. Which in turn means if you deleted something they may still be able to view it depending on how the third party application functions. Essentially because Twitter allows these third party apps to parse the data once they do Twitter has no control whatsoever with what is done with that data once downloaded.
What Can I Do
Really not much other than recommend trust worthy apps to your followers. If they are using some application that hasn’t accounted for this scenario they will see the deleted tweet if for anything a period of time after you delete it. So think before you tweet. Otherwise you’ll be like David Spade in Black Sheep as he describe the fly trying not hit the windshield. “No no not gonna, can’t stop, splat”.