Current cultural evaluations for large language models (LLMs) often reduce culture to single-turn factual recall via MCQs, failing to capture a common use case: users seeking practical help over multiple turns in culturally grounded scenarios. We introduce CultureConverse, a scalable, multilingual simulation and evaluation harness for culturally grounded assistant dialogue that covers 10 East and Southeast Asian regions, 58 subgroup identities, and 7 domains. Each simulated and evaluated episode produces a scored interaction where the assistant assists the user and infers cultural constraints from partial information. The resulting CultureConverse-DS dataset contains 14,610 benchmark (evaluation) episodes and 274,295 oracle-guided (gold-mode) dialogues. In our benchmark evaluation of 18 models, GPT-5 mini achieves the highest assistance quality. Human annotation experiments suggest that our evaluation framework is a sufficient proxy for human judgment. Performance gains from fine-tuning on 27,860 high-quality CultureConverse-DS samples improve in-domain assistance and transfer out-of-domain to cultural MCQ and safety classification benchmarks. We release the harness, both splits, and judge prompts to support interactive evaluation of cultural competency.