Real-world visualization requests are routinely ambiguous, incomplete, or factually incorrect, yet existing Text-to-Visualization (Text-to-Vis) systems assume well-specified inputs and produce charts in a single pass. When queries are imperfect, a system must \emph{interact} with the user to recover the true intent, but no benchmark or method supports this dynamic process. We introduce \textbf{VisInteract}, a new paradigm that reframes Text-to-Vis as interaction-driven intent recovery, and \textbf{VisInteract-Bench}, to our knowledge, that is the first benchmark for dynamic interactive Text-to-Vis, featuring controlled imperfection injection, a leakage-controlled User Agent for realistic multi-turn feedback, and dual-perspective (code and chart) automated evaluation. On the algorithmic side, we propose \textbf{Vis-MCTS}, a Monte Carlo Tree Search (MCTS) enhanced method, introducing improvements over classical MCTS, that \emph{Progressive Widening} to tame the unbounded tool-argument space in tree search, \emph{cross-rollout information sharing} so clarifications and critiques benefit the entire search tree, and \emph{Dimension-Aware Reward Decomposition} that routes scalar user feedback along data-fidelity, visual-design, and intent-alignment dimensions to resolve credit assignment across heterogeneous actions. Extensive Experiments across two LLM backbones show that Vis-MCTS consistently outperforms all Text-to-Vis baselines, improving end-to-end task success by $13.40\%$--$16.27\%$ over the strongest interactive baseline and by more than $5\times$ over non-interactive ones.

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