Generalizable manipulation involving cross-type object interactions is a critical yet challenging capability in robotics. To reliably accomplish such tasks, robots must address two fundamental challenges: "where to manipulate" (contact point localization) and "how to manipulate" (subsequent interaction trajectory planning). Existing foundation-model-based approaches often adopt end-to-end learning that obscures the distinction between these stages, exacerbating error accumulation in long-horizon tasks. Furthermore, they typically rely on a single uniform model, which fails to capture the diverse, category-specific features required for heterogeneous objects. To overcome these limitations, we propose HeteroGenManip, a task-conditioned, two-stage framework designed to decouple initial grasp from complex interaction execution. First, Foundation-Correspondence-Guided Grasp module leverages structural priors to align the initial contact state, thereby significantly reducing the pose uncertainty of grasping. Subsequently, Multi-Foundation-Model Diffusion Policy (MFMDP) routes objects to category-specialized foundation models, integrating fine-grained geometric information with highly-variable part features via a dual-stream cross-attention mechanism. Experimental evaluations demonstrate that HeteroGenManip achieves robust intra-category shape and pose generalization. The framework achieves an average 31% performance improvement in simulation tasks with broad type setting, alongside a 36.7% gain across four real-world tasks with different interaction types.