Ok, so, I thought the same thing everyone else is saying about total chaos at first, but then there were all the stipulations about it being restricted only to teens. Actually, I think it being restricted to teens would actually be the best case scenario if a system suddenly existed with the least chance for something to go wrong. Things would go much more horribly if the system was given to university students, which would be the worst case scenario, and adults 30+ being an intermediate case between the two extremes.
As for the reason teens are the best case scenario, teens actually have a pretty black-and-white sense of morality, and they still have a whole lot of idealism and it hasn't been tainted by a lot of dangerous fanatacism yet like you see in a lot of university students. So, I believe a group of teens are likely to have their bad apples as well as their goodie two-shoes, and the latter will keep the former more or less in check because teens also like a villain narrative and a lot of them might actually be thrilled to go off and fight the villain. However, the ones who do so are also going to come out of it traumatized over the fact they killed an actual person, something they will not have actually thought about before going out to stop the person causing havoc.
As for the government question, yeah, they'd be tipped off within the same week. The reason for that is at least 10% absolute minimum of them will tell their parents, and a lot more will start showing off. News stations will catch wind of this, and so will the government. In the modern day, we also have social media. The government might have thoughts of keeping this under-wrapps, but even if a very small number of teens actually get the system it will still be impossible to contain because a few will be stupid enough to film themselves doing superhuman things and will post it on social media, and even more will be caught on other people's cellphone videos.
I would say the most likely response by the government would be to start screening them for their personality, and separate them into "usable," "threat," and "watch" categories, with the usable ones being the ones who have the strongest sense of duty at wanting to keep the others from harming the community. Those in the "usable" category would quickly be fielded as a sort of police force specifically to handle incidents of others with their power causing trouble. The government would give them military combat training and teach them how to coordinate their efforts, and government researchers would gather data on their abilities and feed that information back to them, so those who are in the government's care will be far more effective and efficient at using their abilities than those who are not in the government's care.
There will be issues that crop up, yes, but our system is very capable of responding to it. However, the REAL threat will come after the domestic issues are ironed out and then the people with this system start getting fielded as actual battlefield soldiers. I would think China would be the first nation to do this, and then the US and other major world powers would be forced to act in kind just to fight against them. This is the stage where real chaos is going to erupt.