The start time of a video within a collection can be set during the process of adding the video to the menu, or from within the button's settings. The start time can automatically be set to the current time using the stopwatch button, or you can manually enter it in hh:mm:ss format.
When you specify a start time for a video, this is essentially creating a chapter point at that time and starting the video from that chapter.
From within the Add Video process:
From within the button setting: