Histone trimethylation on the tail residue H3K9 of nucleosomes is a hallmark of constitutive heterochromatin. The mechanism of how this mark is maintained over cell division cycles remains a topic of ongoing debate. The recent formulation of the polymer-assisted condensation scenario, through which a stable droplet condensate can form as a reaction container for methylation reactions, has offered a novel approach to answer this long-standing question. In this letter, we develop a kinetic proofreading argument for histone tail methylation that builds on the polymer-assisted condensation model and yields support to the idea that liquid-liquid phase separation underlies the reconstitution of heterochromatin over cell division cycles.