If you frame it as an "active shooter" or suspected shooter then the facilities in question are able to be secured without raising suspicion from the general public. Sure, we're actually dealing with spies not a shooting but it's a cover story to protect our petrusite research.
They would panic, they've enjoyed a long period of relative prosperity with no secret police and a much more comfortqable standard of living. Many people from the older generation would still panic at the city being locked down over a terrorist threat and the the younger generation absolutely would. I would also note that if you think no democratic government or republic hasn't lied to protect it's people then you have a somewhat naive worldview. Look back as far as WW2 where even when we knew where the bombs were going to fall in the UK the general public weren't told to prevent a panic. That didn't erode peoples trust in the government, people took it as a given that being told might warn German spies that we had broken Enigma. Hell, in Glasgow/Clydebank my gran says the only warning they got that there would be a raid that night was that you would see the light from the furnaces at the foundry go out.
You'll also have to excuse me if I lack faith in the human herd mentality acting responsibly, all it takes is for the announcement to put people on edge then for a handful of people to start panicking once they see the city is sealed. At that point you have hundreds of thousands, possibly millions of people beginning to panic as word spreads that they've been sealed in a city with what seems to be a major terror threat and no other information. By nature peoples minds will jump the the worst case scenario of a bioweapon or nuke and then your checkpoints are innundated with hordes of people trying to flee once again look back at news reports of the massive lines of cars trying to leave Beijing when it was locked down. Now take that image then add the people who are trying to get out on foot because of the blocked roads.
Yes, in the UK we've had terror threats and let the police deal with it because it was either just a slight raise in the alert level with no stopping of trains or large-scale manhunt or because we knew it was, for example, one man on London bridge with a knife. The Novichok scare too we were told what everything as it unfolded but that it was confined to a single town where people were being tested and the town swept to make sure the nerve agent was gone, at no stage was the town jusy sealed under a "terrorist threat" with no explanation of what was heppening. We knew it was either just a warning to keep an eye out and nothing else or a small-ish scale incident that was already very visibly being dealth with. The way the "oh shit, oh shit" plan deals with it does nothing but leave people uncertain and frightened for no good reason.
After the situation is dealth with we could possibly come clean and I would actually personally prefer to be told after the fact that the manhunt was actually to rounding up of a hostile spy ring. Most of the people I know feel the same way, it's better to know that the security services have bent the truth to avoid a panic while dealing with a problem than to hide everything and let peoples minds run riot.
I said to to go public with the spies so it wouldn't be a nebulous terrorist threat. They fought a bitter war for freedom against a tyrannical fascist regime. They've seen some shit. They know how important it is to work together in a situation like this. They will be pissed if the government starts lying to them.
A long period of prosperity would make the people more likely to trust the authorities and less likely to panic, although it hasn't been that long really since the civil war.
Democratic governments regularly
withhold information for security reasons, i.e. Classified for national security, that is very different from lying. In a functional democracy people go to jail or get fired for lying to the public.
Only in failing or dysfunctional democracies do people get away with that. Given the Helghan actions so far in this quest, it does not seem to fall into that category.
The UK during WW2 didn't see massive civilian panic, despite the freaking Blitz and NAZIs controlling Europe. By and large a pretty good example of how people handle such news, and that is far worse than what I suggested in my plan.
They withheld information about enigma for long term strategic advantage. Though that is still controversial to this day due to the Coventry raid.
Beijing is a terrible example for reasons that are numerous and obvious.
There might be some trouble if they give an evacuation order, though I think that would be isolated incidents. People might panic after an actual nuclear blast. Even then they might not, as people tend to come together to help each other in an emergency.
Mob mentality can get people to do stupid things if they are already in a massive crowd, otherwise there have have to be other underlying issues in a society to get them to riot.
Those cities can stay calm for a day or two while they catch those guys.
The kind of mass panic you're describing is only real in movies. Seriously? A couple of cities get a warning in there area, hear what the government is doing in response and decide to collectively lose there mind and flee the area in mass, rather than say go home and wait for further news.
