Well,
Authorities and experts want to reduce panic to make their jobs (coordination, damage assessment, policing, rescue, etc.) easier and reduce the results of masses reacting panickly.
But authorities also lie time and again and downplay threats to keep panic low (or to make themselves look better, and also because they don't know shit yet, but must still pretend that they are in control).
The sole individual might be more beneficial to panic and get the hell out (not just directly after immediate blow).
The problem is that everybody else panicking will make things difficult, cause mayhem, stampedes, block the highways, limit petrol availability, etc. But that doesn't mean it's not a good strategy at the individual level.
So there's a friction on what might be best survival strategy for each individual, leading to crappy outcomes when adopted by millions.
What I'm getting at is two subtle additions to your comment:
(a) mass panic/exodus might be a crappy response, but it can still be great at the individual level (if only if it could be kept to that). But even if not, the few succeeding in pursuing it, will probably have an advantage over others that meekisly listen to the experts/gov and "stay calm".
(b) experts often don't know whats going on for a long time, have limited input, give contradicting expert advice, and often just flat out corroborate some story to assist the government political decision about handling a crisis.