Answer

I don’t know. It could be understood either way. In the Jerusalem Talmud, Sanhedrin 1:2, it sounds like it was during that same period, since it is speaking about a particular incident (when they went to intercalate the year in Lod):
Rabbi Elazar said in the name of Rabbi Hanina: There was an incident involving twenty-four groups from Rabbi’s household who went to intercalate the year in Lod, and the evil eye came upon them, and they all died in one period. From that time on, they uprooted it from Judea and established it in the Galilee.
Though perhaps there too it was a period of several years during which they did this, and when they saw that people were dying they moved it to the Galilee. But that does not seem to follow from the wording, “There was an incident.”