World models are emerging as critical components for assessing the consequences of actions taken by interactive agents in online planning and offline evaluation. In text-based environments, world models are typically trained and evaluated with single-step metrics such as Exact Match, aiming to improve the similarity between predicted and real-world states, but such metrics have been shown to be insufficient for capturing actual agent behavior. To address this issue, we introduce a new behavior-consistency training paradigm aimed at improving the functional consistency between the world model and the real environment. This paradigm focuses on optimizing a tractable step-level reward named Behavior Consistency Reward (BehR), which measures how much the likelihood of a logged next action changes between the real state and the world-model-predicted state under a frozen Reference Agent. Experiments on WebShop and TextWorld show that BehR-based training improves task-level functional consistency in several settings, with the clearest gains in WebShop and smaller changes in near-ceiling regimes, while preserving or improving single-step prediction quality in three of four settings. BehR-trained world models also reduce false positives in offline surrogate evaluation and improve inference-time lookahead planning over the corresponding supervised world-model baselines. Code: https://github.com/Ricardo-H/behr-wm.