Personality Page is not mainstream Jungian; they seem to be of the opinion that sharing a dominant trait of opposite attitude is most beneficial. More mainstream MBTI sites will tend to agree with Socionics that completely opposite traits are the most complementary (for example Fe and Ti) but disagree on what of these traits correlate to a J or P.

So if you go by the theory that J/P correlates to extroverted conscious traits (the MBTI position), INTP and ESFJ are complementary. If you go by the theory that J/P correlates to the dominant trait, INTJ is ESFJ's dual. Socionics sites tend to take this position.

Note that while these letters should be completely exclusive for introverts, many of the introvert profiles seem to be the same (or suspiciously similar) between the systems, particularly with sensing types. So an (alleged) ISFP MBTI may actually be ISFP in Socionics.

That would imply that someone is wrong/confused. Either the profiles are uselessly vague (Fourier effect, no better than astrology charts for identifying this particular feature), the traits aren't actually real emperical phenomena (Si1 is indistinguishable from Se2), or the traits are being defined differently (such that Si1 in system A is actually Se2 in system B).

To confuse/complicate matters more, all the traits have various features in common with each other: S+T are pragmatic and "hard", T+N are theoretical/consequence-based, F+N are abstract and ideal, F+S are aesthetic and social, just as T+F are judging and S+N are perceiving. So profiles could have varying accuracy while describing surface aspects of real traits, yet not distinguishing them from each other well enough to be useful.

Now, if just you want to use this to find a prospective spouse or best friend who is your dual type, and don't care so much about the theoretical correctness of who is what type, there's a work-around: Find someone who appears opposite on the first three letters, then see if they make you comfortable or not. If they have shared values and a compatible sense of humor, chances are relatively high that they are a dual type rather than a conflict type.