Easy enough. You just need to setup your screen sets.
I created three screens with names Countdown, Tournament, and Break. In the Screen Sets window, I created two screen sets with names "Countdown" and "Break". I'll use the "Default" screen set for Tournament. Add the Countdown screen to the Countdown screen set, add the Break screen to the Break screen set, and add the Tournament screen to the Default screen set. Make sure the Countdown screen set is at the top of the list.
For the Countdown screen set, edit the conditions and set Stage to Before game.
For the Break screen set, edit the conditions and set Stage to During game, and set Level to Break number:. Leave the two other inputs for Level blank. This will make it match any break number.
That's it. Before the tournament starts (whether you're in a countdown or not actually) the "Countdown" screen set will be selected, thus displaying the Countdown screen. Once the tournament is started, the Breaks screen set will be selected if the tournament is currently on break. If not, the selection will "fall through" to the Default screen set, thus displaying the Tournament screen.