To answer the question I looked at the last ten years of games against power conference teams. To control for variance in non-conference scheduling from year to year I only looked at the conference record of each team the year Arkansas State played them and the conference record the year before.
Those power conference teams went a combined 109-66 in league play the year they faced the Red Wolves but only 94-82 the year before. On average, the 22 teams improved by a bit more than half game the year they faced AState.
Overall slightly more than half of the teams, 12 of the 22, had a better season in conference play the year they faced AState than they had the year before. Two had identical conference records compared to the year before and eight did worse.
One reason the improvements have been so noticeable has been because they tended to be so big. Of the 11 schools improving their record, seven improved by two or more wins, four improved by four or more wins and three by five or more wins.
By comparison, of the eight who saw their record drop, four saw their win total drop by 2 or more games but only two lost three or more than year before and only one (2004 Ole Miss) dropped by four wins.
Another reason for the perception has been the improvement shown by recent opponents. The last five years, seven teams improved, two equaled their prior year total, and two finished worse (both 2011 opponents). The biggest improvements happened in the last five years with Auburn improving by seven last year, Missouri improving by five wins last year and Auburn improving by five in 2010 while Illinois finished two wins worse and Nebraska one win worse.
The schools enjoying the greatest improvement over the past ten seasons were: 2013 Auburn going to 7-1 after a 0-8 season, 2013 Missouri going 7-1 following a 2-6 season, 2010 Auburn with an 8-0 SEC record after a 3-5 season and 2008 Alabama improving to 8-0 after going 4-4.
The schools making the biggest drop the last decade were: 2004 Ole Miss 3-5 after a 7-1 campaign and 2005 Oklahoma State 1-7 after a 4-4 season.