The addition of the box amplifies the pressure air exurts on the cone for a given amount of excursion. its like adding more spring to the cone. this lowers compliance.
Looking at the equations for Qms and Qes and Qts, this has the effect of causing changing all three. Qms increase, Qes increases, and Qts increases.
Does this make sense? yes. The system has added more energy storage elements, but has not changed lossy elements. keep in mind that at resonance, where Q is defined, energy is efficiently transfered from compliance to inertia -- the mass of the cone and the compilance of the box/spider are in harmony so to say.
and as compliance drops due to the small box, the resonant frequency increases as well.
as for another example, lets say you pulled the cone outward to some arbitrary position. the cone will now have MORE potential energy due to the increased spring constnat. further, it requires more force to hold the cone outward, thus when released the spring will exurt more force on the same amount of mass, causing it to move to rest faster. because the spring has no potential energy when the cone is at rest, and because the the mass has a higher acceleration, it is clear that the cone will reach its rest point faster and with a higher velocity. Thus higher Fs is expected. without increased losses, the cone will tend to wobble for more cycles.