Existing emotional support conversation (ESC) systems often react directly to surface-level distress expressions, generating reassurance or advice without adequately modeling the underlying psychological needs driving the distress. However, effective emotional support requires an interpretive process that connects what is expressed with why it is expressed and ultimately what support is needed. We argue that current ESC systems lack such an interpretive layer between observation and supportive intervention. To address this gap, we propose HierINT, a psychologically grounded hierarchical interpretive schema for emotional support conversations. HierINT distinguishes observable communicative intentions from the underlying psychological interpretations that drive them, including cognitive appraisals and unmet fundamental psychological needs. Building on this schema, we construct HierINT-Dlg, a dataset with hierarchical interpretive annotations and need-aligned support strategies. We further propose HierINT-CoRe, a collaborative reasoning framework that operationalizes HierINT by jointly modeling psychological interpretation and support strategy planning prior to response generation. Experiments on ESConv and HierINT-Dlg demonstrate consistent improvements over surface-level and intention-aware baselines, particularly on empowerment and personalization metrics. Our results suggest that effective emotional support requires moving beyond reactive response generation toward psychologically grounded need-informed intervention. Our data and code are available at https://github.com/43zxj/HierINT.