Looking at a map of the area around Area 51, I will say that there aren't a million people for miles and miles around, let alone children, let alone one million children exactly the age of 12. Las Vegas Nevada is 2 hours away. The TOTAL population there is about 600 thousand. About 25% are under the age of 18. That's only 150,000, and of those, only a very small percentage will be age 12. (With an even spread of ages, that would be a bit over 8,000). The age range isn't clear. Are we talking toddlers as well? 12 is a good age because, at least then they can reach the pedals of a car.
That means that many of these children will have to travel some distance. The media wouldn't have to be tipped--people would notice that their children are gone long before they get there. We are not living in an era where parents say "I'll see you at dinner kids, go play outside!" Nope.
Let me add as well, that parents often have social circles with other parents who have kids the same age. If one kid is missing, they will start calling other parents. Even if those other parents are somewhat neglectful, they will immediately want to know THEIR kid is safe. Then, they will find their kid is missing. It would not be long before these groups notice all the kids are gone, nor would it be long before those parents inform the police. If even 1/8 of the parents of just the 12-year-olds opt to call the cops in Las Vegas (and I am thinking that's a conservative estimate) they will get 1,000 calls. And the cops will communicate with other, nearby cities. Then they'll notice a pattern and will start calling all the cities in the area. Nothing motivates like kids, so there will be a task-force so very quickly.
Plus, the kids will have to steal vehicles in order to survive the journey at all. That means that some will die in car accidents because they don't know how to drive. And they'll be stopped along the way. So long before they even get to Area 51, there will be incidents of violent children. The media will already know about this, and will already be tracking them.
While the pre-game stuff (getting there) is not in your question, it's highly relevant, because it means this will not be a surprise for anyone, not the military, and not the media.
Because of that, there will be enough time to formulate a non-lethal response, which is exactly what they will do. Law enforcement will likely be asked to help, things will be locked down, and there will be at least one child that's been captured and studied, so they know what they are dealing with. Much of it will still be mystery, but there will be more advance warning than your question indicates. Tear gas, knock out gas, non-lethal weaponry will all be brought to bear. Lethal weaponry will be a last resort, but it will be used.
Remember too that because many of these kids will be travelling from a long way away, and they do have to sleep.
Just checked the national census as well. There are 324 million people in the United States. 12 year-olds make up roughly 1.25% of our total population in the United States. There are 4 million of them in the entire country. That definitely means that you will have to draw from several days journey away. This will involve the population of more than one state. The amount of time means that it will be national news long before they all arrive at Area 51. Going to say that several days will have to pass in order for them all to arrive. The West Coast has some decent population centers, don't think you'll have to delve into the East Coast. Know you've got kids under 12 on that there, but will they be able to travel well? Kids younger than 12 are generally fairly well-supervised. Is it during the school day? On a weekend?
If we use 10% of the population (which is roughly what kids from 6-12 make up) then there are larger numbers, but there are far more problems when it comes to getting the younger kids there, and the younger they are, the more quickly that folks will notice their absence.