The 1960 American Association was made up of eight AAA teams which included the Minneapolis Millers (Boston Red Sox), St. Paul Saints (LA Dodgers), Denver Bears (Detroit Tigers), Louisville Colonels (Milwaukee Braves), Houston Buffs (Chicago Cubs), Charleston Senators (Washington Senators), Indianapolis Indians (Philadelphia Phillies), and the Dallas-Ft.Worth Rangers (Kansas City Athletics). In 1961 the American Association was down to six teams with Charleston being replaced by Omaha and Minneapolis and St. Paul obviously gone.
Here is the article that Halsey Hall wrote for the January 18, 1961 Sporting News. The same Sporting News page has a nice article about the Twins first ever barnstorming trip by Twins publicist Herb Heft that had him traveling 1,312 miles over a four days to sell the upper Midwest on Minnesota Twins professional baseball. I guess you could call this beginning of the Twins Winter caravans that are still taking place 54 years later.