Hybrid organic-inorganic perovskites exhibit high photovoltaic performance and other novel photonic functions. While polaron formation is believed to facilitate efficient carrier transport, the elementary processes of the underlying electron-lattice coupling are yet poorly understood because of the multiscale chemical and structural heterogeneities. Here, we resolve in combined ground- and excited-state spatiospectral ultrafast nanoimaging how structural characteristics are related to both molecular cation and polaron dynamics. We use the observed nanoscale spatial variations of the formamidinium (FA) cation transient vibrational blue shifts as a local probe of the nonlocal polaron-cation coupling. From the correlation with nanomovies of the polaron dynamics, we then infer how a softer more polarizable lattice supports stable polarons and longer-lived residual carriers. This, together with a relative intragrain homogeneity in contrast to high intergrain heterogeneity, suggests pathways for improved synthesis and device engineering, and that perovskite photonics performance is still far from any fundamental limits.