And what causes the lower set of teeth to widen to match the new intermolar width of the upper set of teeth?
Theoretically if the tongue was always resting on the lower jaw, then the lower jaw would already be wide enough, because the upper jaw would become narrow your mandible might be pushed backwards and you'd get an overbite to try and at least make some of the teeth match in width, and thus usable. Once the upper jaw is wide enough, the mandible can be pushed forward again and the teeth can match again.
That's just one theory.
Another is that chewing eventually evens the width out.
When you chew the cusps of your teeth fit inside each other and this can shape how your bite fits.