Penn State was the first domino -- which shouldn't have even happened, but the Big East fubar'd that whole situation in the early 80s. If they had taken PSU in 1981-82, then there probably wouldn't have been a "need" for Miami later on. Anyway....
June 1990 (vote dates, not join dates) - Big Ten adds Penn State (not unanimous; 7-3 vote)
August - SEC adds Arkansas
September - ACC adds Florida State
September - SEC adds South Carolina
October - Big East adds Miami
February 1991 - Big East adds 4 football-only schools (Rutgers, WVU, Virginia Tech, Temple)
The newspaper stories from that era are fascinating. In May 1990, the ACC voted to stand pat. Four months later, they were welcoming FSU.