Atwater stated that there was a "Southern Strategy" developed by Henry Dent in 1968 that focused on the VRA, states rights and forced busing to win Southern votes. The Republicans lost the South in 1968. Nixon won in a landslide everywhere in 1972, and then the Dems recaptured the South in 1976.
The problem for the Democrats "Southern Strategy" narrative was that the "Southern Strategy" as described by Atwater wasn't employed by the Republicans, but by the Independent Party candidate George Wallace, who won the deep South. The Republicans wouldn't take control of the Deep south until Reagan when Atwater said there was no Southern Strategy. So the only part of Atwaters statement that he can vouch for is the Reagan campaign where he states a Southern Strategy was not used... and it was those campaigns that swayed the South into the Republican column.
Likewise, the other Democrat narrative that the Southern Strategy drove blacks to vote Democrat is also not backed up by the data. THe black vote has been solidly Democrat forever, even when the Democrats "Southern Strategy" of "n----r, n----r, n----r" was being used by Democrats in the south.