Don't get why deco is discussed in this incident, as I understand from the OP they missed their safety stop? Seems like they panicked and were still in a panic mode when they surfaced. 30 ft is not a factor for either deco or safety stop, 40 and 19 ft sound more like deco stop depths and 16 for a safety stop in rec diving. IMO due to the situation they were confused and panicked even at the surface and because training said you have to stop at a certain depth and they didn't it was a fear of the unknown more than anything else, still can't figure why they would note 30ft, maybe I'm missing something
You aren't missing anything.
I am not sure, but I think I remember the video in question, and I will describe it. If it is not the video in question, it is one just like it, and we can learn from the one I am describing anyway. In the one I recall, a family is about to begin a dive, and a young boy is wearing a GoPro on his head. They begin a descent. During that descent, the boy begins to plummet rapidly and panic. The rapid descent is blamed on a downcurrent, but other divers in camera rage don't seem to be affected by it. An adult, probably the father, catches up with him and inflates his BCD. At that point the downcurrent stops, and they begin the ascent with ease. Eventually they lose control of buoyancy and go all the way to the surface, at which point they redescend for the missed stop.
The incident is blamed on a downcurrent, but I saw no evidence of one in the video. Here is an alternative explanation for what you see. The boy with the GoPro is inexperienced and likely overweighted. He begins the descent by dumping all the air from his BCD, but as he becomes more negative and his descent speeds up, he does not add air the BCD and panics--an all too common occurrence for a new diver. His father catches up and adds air. Because the boy is overweighted, they have to add a lot of air. As they ascend, that air expands, and the boy who did not add air on descent does not expel air on ascent, so he goes all the way to the surface--an all too common occurrence for a new diver.
Regardless of which story is true, the family does not appear to be highly experienced. The descent to 30 feet is by no means standard protocol for a missed safety stop. No agency I know calls for that. No descent was necessary in this case to prevent DCS--you do not get any appreciable nitrogen load in a minute or two of diving. The most dangerous aspect of the rapid ascent--and it is very dangerous--is the possibility that the boy could suffer a gas embolism from holding his breath during that ascent. In that case, going back down creates the danger of not being able to provide any help in the event symptoms of such an embolism might appear.
In short, in the video I saw, a family without a lot of experience and diving knowledge suffers a cascade of problems, and nothing in the video should be taken as a model for the behavior of anyone else.