I will try to find documents proving that they were founded explicitly to counter the Reformation, but without access to the gilded Vatican Library, I doubt I'll have much success. However, their founding date is dasting when considering.

edit- I found this exerpt but will need to find the citations

The Order was suspected to survive underground and to combat Protestantism and the Enlightenment through "eine Menge geheimer schädliche[r] Gesellschaften". The ensuing discussion soon encompassed the fate of the Order of the Illuminati which had been founded in 1776 by Adam Weishaupt (1748–1830) . He was a professor of canon law at the University of Ingolstadt who took his inspiration from both the Jesuits and the Masons . His "geheime Gesellschaft", as Weishaupt labelled it, sought to win members among the elite and to conquer good positions in order to influence government.