Check a map. Reagan could have lost the entire South in both elections and still won handily. Don't claim credit where it isn't deserved.
They defected from the Dem ranks 25 year ago due to the leftist takeover of the Dem party.
They defected from the Democratic ranks when they found they could do so and still keep their big government, big spending ways.
Texas is not a Big Government state and I think the bias toward big government comes from DC not the States (with some exceptions). Large cities seem to have a Big Government bias everywhere, but especially the North East and West Coast.
My bias against the Lincoln era Republicans comes from ancestors who were "burned out" of AL during Reconstruction. Much of the horrors of the history of that time are not recorded in History books, but has left an indellible imprint on those who moved due to the abuses by the Federal Government. The current parallels frighten me, and I am not easily frightened.
I repeat for clarity that I have never been a Dem.