Data scientists, researchers, and clerks often create web automation programs to perform repetitive yet essential tasks, such as data scraping and data entry. However, existing web automation systems lack mechanisms for defining conditional behaviors where the system can intelligently filter candidate content based on semantic filters (e.g., extract texts based on key ideas or images based on entity relationships). We introduce SemanticOn, a system that enables users to specify, refine, and incorporate visual and textual semantic conditions in web automation programs via two methods: natural language description via prompts or information highlighting. Users can coordinate with SemanticOn to refine the conditions as the program continuously executes or reclaim manual control to repair errors. In a user study, participants completed a series of conditional web automation tasks. They reported that SemanticOn helped them effectively express and refine their semantic intent by utilizing visual and textual conditions.