The spatial segregation of heterochromatin into distinct, membrane-less nuclear compartments involves the binding of the heterochromatin protein 1 (HP1) to H3K9me2/3-rich genomic regions. While HP1 exhibits liquid-liquid phase separation (LLPS) properties in vitro, its mechanistic role in vivo on the structure and dynamics of heterochromatin remains largely unresolved. Here, using biophysical modeling, we systematically investigate the mutual coupling between self-interacting HP1-like molecules and the chromatin polymer. We reveal that the specific affinity of HP1 for H3K9me2/3 loci facilitates coacervation in nucleo, and promotes the formation of stable heterochromatin condensates at HP1 levels far below the critical LLPS concentration observed in vitro in purified protein assays. These heterotypic HP1-chromatin interactions give rise to a strong dependence of the nucleoplasmic HP1 density on the HP1-H3K9me2/3 stoichiometry, consistent with the thermodynamics of multicomponent LLPS. The dynamical crosstalk between HP1 and the visco-elastic chromatin scaffold also leads to anomalously-slow equilibration kinetics, which may result in the coexistence of multiple long-lived, microphase-separated heterochromatin compartments. The morphology of these coacervates is further found to be governed by the dynamic establishment of the underlying H3K9me2/3 landscape, which may drive their increasingly abnormal, aspherical shapes during cell development. These findings compare favorably to 4D microscopy measurements of HP1 condensates that we perform in live Drosophila embryos, and suggest a general quantitative model of heterochromatin formation based on the interplay between LLPS and chromatin mechanics.