The dichotomous types carry over from those systems to Socionics. If you were an 'actual' XXXX, in Socionics your theoretical type is still XXXx(but because of erroneous typings, faulty tests and general difficulties your type may be totally different).
This is something that people don't usually talk about and get straightened out as they cross over to Socionics and they end up representing the Quasi/XXXy of their actual type. For example, if you were consistently typed as ESFP(Extraverted, Sensing, Perceiving) or INTJ(Introverted, Intuitive, Judging) in MBTI, you would assume ESFp/SEE or INTj/LII in Socionics.
Still, keep in mind the above quote - that, in reality, and not theory, your type could still be inaccurate, but as for theory, type translates according to what I've demonstrated.