Each digital tacho can be preset for different functions at key on/off. A VDO must be done at a calibration centre. A Stoneridge can be done with a company card. They can be set to auto select break or work at either key on or off.
However, this isn’t some magical trick to catch you out. If you are on break and need to turn the ignition on, then do so and be prepared to simply press the mode button back to break - it’s not difficult. In fact, at autom mode selection it should flash the mode a few times before it actually changes, therefore allowing you to return to break.
Because the tacho only records complete minutes, turning the key, selecting break again, will have no effect on your break.