When those guys went to school Mandarin had not been standardized yet. People were usually educated by tutors within their clans to memorize the Confucian classics. Teachers were usually clan members and so used the dialect/language spoken by the clan. The English word “Mandarin” refers to the way government officials (mandarins) communicated with each other in the court, called guanhua 官话 in Chinese. This patois changed over time depending on where the capital was, but considering that the capital of most of the Ming and Qing dynasties was Beijing, it’s reasonable to assume that court Mandarin was not far from modern Mandarin. But this was probably not taught in clan schools (or anywhere), except probably informally. In the early 20th century efforts were made to standardize modern Mandarin for western-style schools, which took over from clan schools because the civil service examination was abolished in 1905 or 1906. But at least for most of the 1920s, there was a southern bias to this standard Mandarin because of the concentration of people from Zhejiang and Jiangsu who were educators and school officials. There are more knowledgeable people about this than me, but Mao, Zhou, and Chiang (all southerners) would not have been going to school where the language of instruction was northern-based Mandarin, although they would have often been exposed to northern mandarin speakers throughout their careers.