For flat sealed units such as hockey puck
hand bearing compasses, the dip will cause the card to ground out on the casing giving random erroneous readings. There is nothing to adjust on these compasses. If you are desperate you might be able to hold the compasses tilted at some appropriate tilt and get a good reading.
For ship's compasses gimballed inside a ball, the card will not be level but the reading should be correct or very close to correct. Because of the tilt the gimballing may ground out at less heel on one tack or the other. Most ship's compasses are adjustable and you should be able to readjust the compass for the correct hemisphere.
Directions for compass adjustment are in the 1984 Bowditch, I don't know about newer editions. There is an online edition of unknown vintage available for free at
or just the compass chapter at http://www.irbs.com/bowditch/pdf/chapt06.pdf