I don't think Reagan turned him into anything. There was a long line of more or less conservative Southern Democrats and Perry seems to have been bringing up the rear.
Charlie Wilson (of the Tom Hanks movie fame) was another. They certainly weren't against Reagan's Cold War policies. They were just yellow dog Democrats following a 100-year tradition.
Having a father who took him to Sam Rayburn's funeral probably did something to keep Perry in that tradition. He's not my candidate for anything, but I doubt he was acting out of a strong negative reaction to Reagan.
If you were alive, fully grown, politically oriented, and remember the 1980s, there was no way not to have a strong reaction to Reagan, you reacted either strongly positive, or strongly negative, Perry became an active Democrat leader and campaigner for Al Gore.
Sam Rayburn died in 1961, it didn't influence anyone during the Reagan Revolution.