Training multimodal agents via reinforcement learning for knowledge-intensive visual reasoning is fundamentally hindered by the extreme sparsity of outcome-based supervision and the unpredictability of live web environments. To resolve these algorithmic and environmental bottlenecks, we introduce ProMMSearchAgent, establishing a novel Sim-to-Real training paradigm for multimodal search. We decouple policy learning into a deterministic, local static sandbox. Crucially, to learn effectively within this constrained environment, we propose an introspective process-oriented reward. By probing the agent's own parametric knowledge boundaries, we generate dense behavioral metadata that explicitly rewards the correct cognitive decision, initiating a multimodal or text search only when visually or factually uncertain. Extensive experiments demonstrate that our locally-trained policy transfers zero-shot to the live Google Search API. ProMMSearchAgent achieves new SOTA performance, outperforming MMSearch-R1 by +5.1% on FVQA-test, +6.3% on InfoSeek, and +11.3% on MMSearch.