What would happen to the rod if the magnets were turned upside down?

If you reversed the direction of the magnetic field by turning the magnets upside down, then using Fleming's left-hand rule you can see your first finger will be placed in line with the direction of the magnetic field (i.e. north to south), or in the opposite direction to before.

The second finger will be placed in line with the direction of current in the wire, the same direction as before.

Your thumb will now show you the direction of the motion of the carbon rod.

In this case it will be in the opposite direction to the first left-hand experiment.