It may be because you have the mission settings in the Litchi app set to curved turns rather than straight line. Curved turns do not allow for actions at waypoints, which would allow for the switch to video and recording of that video for specified times at each waypoint.
In order to make the switch from the first waypoint photo to video, you would have to use straight line in the settings and then change the actions at the subsequent waypoints to video, including the length of time you loiter or remain at the waypoint collecting video at each waypoint.
Another way to do it would be to fly manually to the first waypoint location and after taking your still photo load and fly the mission using curved lines and video from the start point of that mission. Again, you would not be able to stop and take various actions if the turns were curved, the video would be continuous during the length of the mission. If you use this method, if there is a disconnection, the flight will continue until the last mission command, i.e., RTH, reverse the mission,, hover or land.
Hope this helps.