Today, fostering media and information literacy (MIL) among citizens is essential for preserving democracy. The effectiveness of scalable interventions, particularly those employing lateral reading, a fact-checking heuristic, is well recognised. Our digital workshop, designed to model lateral reading from a user's perspective, has proven beneficial in educational settings and has garnered expert endorsement. Addressing recent scholarly calls to understand the underlying mechanisms of successful MIL interventions, our study is anchored in Cognitive Load Theory. We examine how different instructional modalities in our workshop influence engagement with lateral reading and how effectively it is executed. The study separates implicit text feedback and hands-on video instructions, previously combined, in a full-factorial design using a parallel-group RCT. We analysed the responses of 178 upper-secondary students in the online workshop and conducted a detailed video analysis of 30 students participating in a controlled environment at their schools. Our findings reveal that hands-on video instructions notably enhance both the engagement and effectiveness of the lateral reading heuristic. This study underscores the significance of a human-computer interaction perspective in designing more impactful media and information literacy interventions.