The solidification of heavy metals in the municipal solid waste incineration fly ash was realized by the hydrothermal treatment with mineral additives added. The experimental results showed that the addition of SiO2 at 200 °C with the NaOH concentration was 0.5 mol/L attributed to the formation of fibrous tobermorite and effectively reduced the heavy metals toxicity of hydrothermal products, especially Pb and Cu. When SiO2 and Al2O3 were both introduced, the generated katoite and sodalite showed a better curing effect on Zn at lower NaOH concentrations. Further, the dynamic correlation between the tobermorite formation and heavy metals solidification was explored. It was found that the heavy metals in fly ash were first dissolved into the alkaline liquid phase and then transferred into the solid phase as the treatment proceed. The solidification of Pb which finished before 8 h was mainly due to the encapsulation of the tobermorite precursor before crystallization, while that of Cu which lasted over 48 h mainly relied on the adsorption and cation exchange effect caused by the formed tobermorite. Therefore, selecting the appropriate mineral addition scheme and hydrothermal time according to the fly ash components and heavy metals categories can effectively improve the curing cost performance.