Customized presentation is gaining more popularity. The MPEG media transport (MMT) system provides flexible media unit encapsulation and comprehensive control signaling to support multiple content types that may be useful during the customization. Existing legacy methods, however, did not take into account relations within media asset and the combination of diverse media components. Furthermore, considering more complex scenarios such as transmissions over heterogeneous networks and various user behaviors, a flexible timeline control scheme is essential for achieving smooth and precise playback. For better catering to the requirements of customized presentation, this paper proposes a new timeline scheme that can quickly respond to user interactions and generate the timeline via proper signaling. Experiments validate that the newly developed method successfully controls the presentation process of customized requests in MMT system.