Text-to-Visualization (Text-to-Vis) translates natural language queries into visualization query languages, enabling non-expert users to perform data analysis. However, most existing methods follow a one-shot paradigm that requires users to specify all visualization details in a single round, often leading to cognitive overload and incorrect visualizations. In this paper, we propose PMVis, a progressive multi-turn paradigm for text-to-vis, where users' intents are refined through multi-turn interactions. To support research in this paradigm, we construct PMVisBench, the first dataset designed to capture the progressive and iterative nature of real-world user queries. It is built through VQL simplification and NLQ reconstruction, with explicit rule constraints to ensure each intermediate VQL remains valid and meaningful. Building upon PMVis, we further introduce PMVisAgent, an agent-based framework that simulates realistic user-system dialogues. PMVisAgent consists of a User, a System, and a Validation Agent that performs verification and repair via a ReAct-style tool-use loop to mitigate error accumulation across rounds, with explicit interaction and verification rules to ensure reliability of the multi-agent system. Extensive experiments on PMVisBench demonstrate that PMVisAgent significantly outperforms state-of-the-art text-to-vis baselines. It achieves up to 17.57\% and 23.21\% improvements in execution accuracy in single-table and multi-table settings, respectively, while ablation studies confirm the importance of combining progressive interaction with clarification. The code is available at https://github.com/wxxv/PMVis.

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