It's a difficult line to draw accurately - the line between "modern" pass-happy football and the option, 3 yards and a cloud of dust football played before that. Passing leaders have gradually improved bit by bit as time has progressed, but any line drawn would be more recent than many would think. You wouldn't have to go back to the 70s.
BYU started it, unless you count Tulsa before them. Then Miami got into the big passing offense, and others after them. Florida began it in the SEC with Spurrier. Iowa and Cal had some big-passing teams in the 80s, but that was mostly due to talent at the position more than anything. The Big 8 was late to the passing party.
If I had to set a hard line, I'd say 1992/1993. In the years before that, there'd be 3-4 QBs with a 150+ rating each season, sometimes less. In 1992 there was only 1, but that was just a down year. 1993? 13 QBs finished 150+, which dwarfs the seasons before it. People had time to see Miami succeed with it, then with FSU and Florida, not just winning, but winning by very big scores. I think the rest of the country dove in after that (in terms of not just passing, but passing for success).