It doesn't matter if the black hole is rotating, since Jupiter is already rotating. Since Jupiter's mass already has a rotational moment of inertia, it will continue spinning as it is sucked in.
Also, conceptually, the total mass of Jupiter has not changed by very much by introducing a black hole, so there is almost no additional sucking force that is pulling Jupiter's mass into the center.
Since the surface area of the black hole is so small (0.005 m^2, at least at first), you won't actually be losing that much mass, relative to the entire mass of Jupiter. So the loss of mass won't be that fast.
Jupiter isn't collapsing right now because the force of gravity is being counteracted by the pressure of the particles that are already in the center. As those particles interact with the event horizon and 'dissapear', other particles will move to take their place. However, consider that if you divide Jupiter into an infinite set of spheres, nested one inside the other, the spheres get larger as you go towards the surface. Therefore, as mass is lost to the black hole, the mass being sucked inwards will be compressed and heated. This heating will in turn increase the pressure in the regions near the black hole, and will thus slow the rate of collapse of the planet.
None of these considerations really change the outlook for the planet, as Mike Scott put it, but the planet will die a spinning, glowing white hot death, as opposed to just imploding.