I really really doubt that an instructor taught him to take off his mask and put it around his neck after making an emergency accent.
I am not so sure. In fact, if an instructor said something like that, I might say, 'Good on him!' - not that the mask should be put around the neck specifically after an emergency ascent, but that around the neck is better than on the forehead.
I think the issue is the 'mask on forehead as a sign of distress' situation. I DO think that panicked / stressed divers who make an abrupt ascent to the surface are somewhat likely to do one or two things (or both): a) spit their second stage out of their mouth, as they gasp / gulp air, and b) push their mask up off their face, and onto their forehead (or off their head altogether) to breath in as much air as possible. I have seen this happen more than a few times. Now, I don't see a 'mask on forehead' as an intentional sign that someone is panicked, or is distress - people who are panicked are seldom able to intentionally signal anything. But, I do see a mask dropped down around the neck as a possible indicator that someone is not panicked, that they have done it purposefully. So, it is quite possible that the diver's instructor said something like, 'Don't push you mask up or your forehead, others might think you are in distress. Better to drop it around you neck, or reverse it on your head.'' So, the diver in the video may not have been actively taught that it was a sign that he was 'OK'. Rather, he had been taught to do something that would avoid creating a possible impression that he was not OK, i.e. in distress.
Mask position is not an accepted, universal sign of anything, as far as I know. And, more than a few experienced divers may say, 'I have put my mask on my forehead at the surface for many years, and it has never been an issue.' Nonetheless, I tell students in my classes - OW, AOW, whatever - 'When you are at the surface, I DO NOT want to see your mask on your forehead!' Part of the reason is that I don't want the 'panicked diver scenario' possibility to even be an issue. But, of the three positions a diver might use when they want to take the mask off their face - a) pushed up on the forehead (with the mask strap not under much if any tension), b) dropped down around the neck, and c) reversed on the head (with the mask strap under tension), the position in which a mask is most likely to be lost, is on the forehead. And, since a lost mask on a student in one of my classes is likely to be associated with some delay (including having other divers drop down to look for it, if depth / conditions permit), I let the students know that the forehead is not an acceptable location, if they feel the need to take the mask off their face at the surface for whatever reason.