Thrasyllus, Dorotheus and Valens used a sidereal zodiac with the the equinoxes and solstices at the 8th degrees, thus their antiscia are Gemini-Leo, Taurus-Virgo, Aries-Libra (not according to Thrasyllus because of the opposition), Scorpio-Pisces, and Sagittarius-Aquarius. Cancer and Capricorn are left without schema, because they have no counterpart in any sidereal zodiac. Their contra-antiscia are Taurus-Pisces, Gemini-Aquarius, Cancer-Capricorn, Leo-Sagittarius and Virgo-Scorpio. Aries and Libra are left without schema, because they are equinoctial. These relationships were used to modify the interpretation of existing sextiles and trines.
However, Ptolemy, Paulus and Rhetorius who used a tropical zodiac with the equinoxes and solstices at the 1st degrees also used the same antiscia and contra-antiscia. Ptolemy explains the antiscia with the fact that the beginning of Gemini has the same daylight as the beginning of Leo and so on, and the contra-antiscia - from the rising times of the beginning of the signs - rather than their end.
Ptolemy was the most brilliant astronomer (and astrologer) of antiquity. Obviously he knew what he was doing and wasn't just using some ''outdated remnant''.
Keep in mind that all these schemata break at the equator.