In SimplyTweet 2.3, you can now configure the sound that is being played when you receive a push notification. It's the only configuration which is done from within SimplyTweet, and not in the Settings app. The reason is technical: there is no way to preview the sounds if you do it in the Settings app. (I know Apple lets you do that in their own app, but I'm mortal).
There are 2 types of push sounds. "Not Active" refers to the sound played when SimplyTweet is either not running, or when it is running, but the screen is off. "Active" refers to the sound played when SimplyTweet is running and the screen is on.
That's it. Enjoy the bird chirpings! (There's a None sound if you really hate birds or any kind of sound.)