I have had a few incidents that thankfully weren't too bad but have sent out the text to my family. After you have cleared the warning it returns back to your default watch screen with no indication that any activity took place.
There is no acknowledgment inside the app either that you have had an "incident" or that there is any kind of partial activity data, everything just acts as though you never went out on any kind of activity.
Like you say, it isn't good at all. I have switched that stuff off now anyway as along with those questionable choices above I was sick of having it give false positives and scrambling to try and cancel it, or not realising it was giving a false positive and then my family worrying and me losing my data for that session.
Although obviously not ideal in all situations I would rather an option to be able to manually send coordinates should I have an incident I needed help. That wouldn't help in situations where I wasnt conscious but neither is having it switched off because its functionality is annoying.