Actually, one of the movements we see is that as the conquering Christians sweep southward, both Mozarab Christians and Jews from Islamic Iberia start to move north into their expanding territory. In sources, it's particularly visible with Jewish intellectuals and merchants, and with Christian farmers. (The fleeing farmers in particular were crucial for bringing southern dry-farming techniques northward and aiding the growth of the Christian Iberian economy.)

But this is not because the conquering Christians are so awesome. The Reconquista coincides with the rise of the Almoravid and then Almohad dynasties in North Africa and Iberia. The new rulers were much less tolerant of religious diversity--both among different religions and actually among less zealous Muslims, too. There were even some campaigns of forcible conversion among the Jews, at least, as we know from the scholars' movements to the generally-less-tolerant-than-the-Umayyads-had-been Christian north. In many areas, like Valencia, on the eve of conquest there was basically no remaining Mozarab population to have an opinion. They had converted or fled the increasing intolerance.

ETA Sources: Since there is probably a direct address to this question, I'm almost embarrassed at what I had to put together for a two paragraph answer. Still: Constable, Trade and Traders in Muslim Spain; Burns, Muslims, Christians and Jews in the Crusader Kingdom of Valencia; Glick, Islamic and Christian Spain in the Early Middle Ages; Hamilton, Representing Others in Medieval Iberian Literature