According to the lunar calendar, the ancients divided a year into four seasons, each with three months, totaling twelve months, and matched Meng Zhongji with the three months of each season. "Every four-year-old has a spring, summer, autumn and winter, and each has Meng Zhongji, with October in his name" (Yi Zhou Shu Zhou Yue).
When expressing months, Meng means the first month of each season, Zhong means the second month, and Ji means the last month, that is, the third month. Of course, it's all about the lunar calendar, which is the lunar calendar.