So, before I address the rotational aspect of your question, we should see how a magnet would behave when it is moved through the magnetic field without spinning. In this case, it's best to draw out the field lines of our magnet (A) and the magnetic field (B).

The magnet is going to want to align its field lines of the magnetic field it's moving through. So if we consider the three positions:

(1) to the left of the magnet
(2) in the center
(3) to the right

The magnet will tilt such that it aligns itself to the magnetic field lines as shown in the picture (link named "magnet" above).

Now for the rotational aspect, when you spin a magnet about the axis running through the two poles (C), an electric field is created. This field however, doesn't interact with the magnetic field so it should still tilt the same way as the non rotated example. There's probably some resistance to the tilting of the magnet from rotational inertia. I think a more interesting case would be if we rotated the magnet as shown in (D). This type of rotation would cause changes to the magnetic field around the magnetic as it is spinning. So when the magnet is rotated in this way, it will spin faster, as the north pole is rotated towards the south pole or away from the north pole. The rotation will slow down as the north pole is rotated away from the south pole and towards the north pole.