Clemson was a member of the SEC from 1920 - 1953.
https://www.clemson.edu/institutional-effectiveness/oir/resources/acc.html
I think you are confusing the Southern Conference with the South Eastern Conference, a mistake I have made in the past. Clemson was never part of the SEC, but was part of the Southern Conference, at least, that’s how I’m understanding your links.
I’m not an expert on the conferences by any means, but unless there was an error on the second link, Clemson is not mentioned in this section.
From your second link:
***The 13 members west and south of the Appalachian Mountains reorganized as the Southeastern Conference at the annual SC meeting of Dec. 8-9, 1932, in Knoxville. The 10 coast members remained in the Southern Conference. Dr. Frank L. McVey of Kentucky was elected president of the new conference whose charter members were: Alabama, Auburn, Florida, Georgia, Georgia Tech, Kentucky, Louisiana State, Mississippi, Mississippi State, Sewanee, Tennessee, Tulane and Vanderbilt. (Sewanee withdrew Dec. 13, 1940, Georgia Tech on June 1, 1964 and Tulane on June 1, 1966). McVey held an informal meeting of the school presidents in Birmingham Feb. 16, 1933, then the first full meeting in Atlanta Feb. 27.
Faced with the task of conference realignment after competing with 10 members since 1966, the SEC welcomed the University of Arkansas on Aug. 1, 1990, and the University of South Carolina on Sept. 25, 1990. Both joined the SEC on July 1, 1991.
Fully incorporated into conference competition by 1992, Arkansas and South Carolina participated in SEC championships for all sports except football during the 1991-92 academic year. The SEC was again at the forefront, introducing football, basketball and baseball divisional play and the nation’s first-ever Division I football championship game.
The conference welcomed Texas A&M University on Sept. 25, 2011, and University of Missouri on Nov. 6, 2011, in the only other expansion in SEC history. Both joined the SEC on July 1, 2012 and competed in their first year in all conference sports in 2012-13.***