the cone of the driver that makes the fundamental ALSO makes the overtones. They are not generated electronically, they are generated physically, relative to the fundamental
Whatever gave you that idea? Your first video is no help at all. Don’t you understand that the harmonics are part of the audio signal which is separated into frequency ranges by crossovers?
Yes, harmonics are not (usually) generated electronically, they are generated by the originating instrument and are what gives each instrument its sound signature.
When a piano, for example, plays a low note, the fundamental may be sent to the sub-woofer but the first harmonic will go to the woofer, the second harmonic maybe to a mid-range driver and some very high harmonics will be handled by the tweeter.
They are absolutely not all handled by the cone of the sub-woofer.
There are special considerations. If the sub-woofer cone does not follow pistonic motion, but experiences cone breakup, these will show as nasty higher frequencies generated by the sub-woofer cone.
As several others have pointed out, cross-overs are not brick-wall filters so there is some bleed through of higher frequencies.
Some distortion is generated electronically and is sometimes encouraged, for example in valve amplifiers