In the Babylonian calendar, which Jews used in the late pre exilic, exilic, and early post exilic periods, the 1st of Nisannu always fell after what we would consider to be the equinox (though not necessarily after the equinox as the Babylonians counted it.) By the Herodian period, it is not certain that Judea is following Babylon any more. Josephus says that 14 Nisan occurs "when the sun is in Aries" (Antiquities 3.10.5), that is, on or after the equinox. In the Talmud, the equinox is given as one of three conditions, two of which must obtain for an intercalation.
Our Rabbis taught: A year may be intercalated on three grounds: on account of the premature state of the corn-crops; or that of the fruit trees; or on account of the lateness of the equinox. Any two of these reasons can justify intercalation, but not one alone. (Tractate Sanhedrin)
The Tosefta gives a rule for intercalating on account of the equinox:
The year is not to be intercalated unless the spring equinox is still distant the greater part of a month. How much is the greater part of a month? Sixteen days. R. Jehuda says: Two thirds of a month, twenty days. T. Sanhedrin 2.7.
The Rabbinic calendar, which dates from the period C.E. 700-950, though a late Jewish tradition gives it a date in the 4th century C.E., seems to have been designed always to put the 15th or 16th of Nisan after the equinox. And due to a slight solar drift in the Rabbinic calendar, the 16th of Nisan is now always after the equinox. The 15th of Nisan can not now fall before March 26th in the Gregorian calendar, and in the 8th, 11th, and 19th years of the 19 year cycle, the 16th of Nisan can be a month after the equinox. as it was in 2016.