The multiple drivers in a 2+ way speaker, or when using a subwoofer plus speakers, always has overlap in the frequencies covered. That's how things are designed, on purpose, in order to get the best sound.
However when using a subwoofer, it depends on whether or not you have bass management or not. If you do, then the preamp or crossover will split the signal at the crossover point (there is still overlap). If you do not, then you'll end up running full-range to both the speakers and the subwoofers, and will need to calibrate based on that fact.
Subwoofer DSP room correction does not implement a crossover. A preamp with bass management will implement a crossover.
However when using a subwoofer, it depends on whether or not you have bass management or not. If you do, then the preamp or crossover will split the signal at the crossover point (there is still overlap). If you do not, then you'll end up running full-range to both the speakers and the subwoofers, and will need to calibrate based on that fact.
Subwoofer DSP room correction does not implement a crossover. A preamp with bass management will implement a crossover.