Autonomous multimodal language models are rapidly evolving into web agents that can browse, click, and purchase items on behalf of users, posing a threat to display advertising designed for human eyes. Yet little is known about how these agents interact with ads or which design principles ensure reliable engagement. To address this, we ran a controlled experiment using a faithful clone of the news site TT.com, seeded with diverse ads: static banners, GIFs, carousels, videos, cookie dialogues, and paywalls. We ran 300 initial trials plus follow-ups using the Document Object Model (DOM)-centric Browser Use framework with GPT-4o, Claude 3.7 Sonnet, Gemini 2.0 Flash, and the pixel-based OpenAI Operator, across 10 realistic user tasks. Our results show these agents display severe satisficing: they never scroll beyond two viewports and ignore purely visual calls to action, clicking banners only when semantic button overlays or off-screen text labels are present. Critically, when sweepstake participation required a purchase, GPT-4o and Claude 3.7 Sonnet subscribed in 100% of trials, and Gemini 2.0 Flash in 70%, revealing gaps in cost-benefit analysis. We identified five actionable design principles-semantic overlays, hidden labels, top-left placement, static frames, and dialogue replacement, that make human-centric creatives machine-detectable without harming user experience. We also evaluated agent trustworthiness through "behavior patterns" such as cookie consent handling and subscription choices, highlighting model-specific risk boundaries and the urgent need for robust trust evaluation frameworks in real-world advertising.