This paper reports on some data on the effects of screen-based interactivity on children's engagement with storybook apps during family shared book reading that were gathered in a 2-year, small-scale ethnographic case study in Spain. Data analysis focuses on the complex interplay between the storybook app's interactive features and the children's responses to them. Our findings show that interactive elements increase the child's autonomy, as they tend to promote the importance of the reader, positioning him or her as a collaborator, storyteller, an author or an internal character in the fiction; something that can materialise in exciting narrative strategies that can trigger powerful responses to digital literary texts in emergent readers, including playing, creating new fictions or engaging emotionally with the story. Finally, we argue that the Reader Response models that have been used over recent decades to understand children's reading experiences with storybooks need to be revised to better understand their current experiences with interactive texts.