Causation goes the other way: Reagan's prioritization of tax cuts over public education led to tuition increases, which lead to an increased demand for loans to pay the higher tuition.
I don't see it that way. The 80s "greed is good" mentality laid the groundwork for the fleecing, but that was not Reagan's fault other than perhaps that administration was the time when financialization of everything began. Think "junk bonds" then think "loans that can't be discharged in bankruptcy."
Reagan was the one who re-introduced tuition (at all) to the University of California system in the first place.