Doesn't this mean there is an overlap of what the subwoofers are covering and what your speakers are covering so both your speakers and sub are producing any music below 120 or 100?
Yes. That's the idea. The more overlap the better. The whole point of multiple subs (Swarm, distributed bass array, etc) is the more places the bass comes from the smoother, faster, and deeper the results.
Doesn't this cause distortion?
Only in the sense that on paper it looks like the timing is all wrong. Which would indeed be a very serious problem, if we were talking about midrange and treble. Precise equidistant symmetry is absolutely critical in order to get good imaging from the stereo speakers.
Bass however is completely different. At 20 Hz for example a human being cannot even hear the sound AT ALL at less than one full wave. That's 1/20th of a second. Cannot hear it at all! We simply cannot localize low bass anywhere near like what we can with higher frequencies. Read up on it. Its two completely different animals.