I have found a workaround - it may well be the actual solution - but it seems to have worked.
In Storyline, and then in video mode, the playback is set to automatic, but I changed that setting to "clicked".
Clearly it means that when you put the file into Rise, the video(s) start up automatically, even if you haven't reached that stage of the Rise course - so a lesson with multiple videos has them all starting as soon as the Rise lesson is opened. By changing the setting in Storyline to "clicked" it is a manual process that learners need to press play.
The play/pause/stop buttons were in place, so these now have an actual function for learners.