Neoproterozoic cap carbonates are characterized by “anomalous” sedimentary features, including sea-floor precipitates, represented by aragonite pseudomorph cement crusts and crystal fans. These features are found in restricted periods of geological history, and their generation in the context of the Neoproterozoic has been attributed to very specific postglacial conditions leading to alkalinity oversaturation. New sedimentary and geochemical results on well-preserved Neoproterozoic deposits of aragonite pseudomorph crystal fans at the base of the Sete Lagoas Formation (Bambuí Group, central Brazil) are reported. The micrite-settling facies shows the highest abundance of crystal fans, arranged in centimeter-scale layers interfingered with the micrite matrix; this facies is interpreted as a result of postglacial calcium carbonate oversaturation in restricted areas characterized by marine dysoxic waters. A numerical model constrains the kinetics of formation of aragonite crystals or micrite by calculating the induction times and precipitation rates of both carbonate species for postglacial conditions of elevated temperature and high atmospheric pCO2. In these conditions, the Mg/Ca ratio of the Neoproterozoic seawater is calculated at ca. 1.2. Alkalinity oversaturation is monitored by a variable evaporation degree. Aragonite formation is kinetically favored, and the discrepancy between calcite and aragonite precipitation rate is greater as atmospheric pCO2, hence alkalinity, is higher. These modeling conditions do not preclude the contribution of incomplete organic-matter degradation to alkalinity as suggested by negative carbon isotope signatures. In addition, the large number of aragonite–micrite pairs suggests a seasonal or paleoclimatic forcing. Other cases of abiotic aragonite precipitation through time are also briefly examined by comparison.