In this work, we performed temperature-dependent Raman spectroscopy studies on single crystals of three layered metal thiophosphates: CuInP2S6, CuCrP2S6, and CuInP2S6-In4/3P2S6 heterostructures. These materials are emerging multiferroics, with CuInP2S6 and CuInP2S6-In4/3P2S6 exhibiting room temperature ferrielectric polarization while CuCrP2S6 is both anti-ferroelectric and antiferromagnetic at low temperatures (<145 and <30 K, respectively). We studied two prominent peaks in the Raman spectra of these compounds, namely their phosphorus-phosphorus (P-P) and phosphorus-sulfur (P-S) stretching modes. First order linear fits to the mode softening yielded coefficients similar to other layered materials. Furthermore, analysis of the phonon decay mechanism revealed the dominant role of anharmonic effects rather than thermal expansion. In particular, the decay of the optical phonons was found to be governed by three-phonon processes in CuInP2S6 and CuCrP2S6 and by the four-phonon process in the CuInP2S6-In4/3P2S6 heterostructures. These phonon lifetimes were found to be less than 1 ps, indicating high scattering rates and highlighting the high degrees of anharmonicity in these materials.