At what halachic hour did chazal think the korban mincha was actually offered, assuming ideal circumstances? I.e. when they say "from the time of the mincha and onwards" (e.g. Rosh Hashana 4:4) what hours do they have in mind exactly? Does this just mean from the beginning of mincha ketana onwards or something else?
What is called the time of mincha is actually the time of the afternoon tamid (for explanations of the name, see Tosafot Pesachim 107a). The afternoon tamid was generally slaughtered at eight and a half hours into the day and sacrificed at nine and a half hours into the day (Pesachim 5:1; see there for when it was slaughtered earlier on Erev Pesach). Since Rosh Hashshana 4:4 is due to the levites' song, it makes sense that the intention here is while the tamid is sacrificed, which is when the levites sang (during the pouring of wine on it).