I found this "seeking" clarification misleading because it is not necessarily correct. It is more correct to say that the magnetic needle will always align so that its south-North direction (i.e. its magnetic moment) points in the same direction as the
local magnetic field. I stress the word "local".
Study the diagram below. It's a schematic of the Earth showing its magnetic field lines as if they were generated by a bar magnet. The arrows in various places indicate the direction of the local magnetic field and the dashed circle represents the spherical Earth. Imagine walking on the dashed circle holding a compass needle. It will align itself with the field lines so that in the northern hemisphere the north pole of the needle will be "seeking" the south pole of the Earth, that's true enough. At the Earth's magnetic north, the needle's north will point straight down to the Earth's magnetic south. However, near the magnetic north of the Earth, which is near the geographic south, the needle's north will point away from the Earth's magnetic south so it's more correct to say that in the southern hemisphere the needle's south is Earth north "seeking".
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The explanation above was deliberately constructed to show you how confusing this "seeking" business could be. The best way to understand it is to have a clear picture of (a) what the magnetic field looks like in 3d space and (b) where you are in that 3d space. Then apply the principle that the needle will line itself with the local field and consider the orientation of the needle at different locations, something like what is shown in the hyperphysics link, posting #6, but with the Earth instead of a solenoid. Generalizations trying to explain which way the magnetic needle will "always" point are fraught with pitfalls. This is one of the situations where a picture is worth a thousand words.