When the lawyer, Wesley Evers, shows Officer Nolan the Emergency Alert that was sent to many cell phones, the date on the cell is "Sunday November 3". Court is not in session on Sundays, but that is the day this episode originally aired.
The courtroom scene shows everybody, including people in the gallery checking their phones when the alert goes off. Most courtrooms only allow judges and lawyers to have phones in the courtroom.
BMEWS - Or the USAF Ballistic Missile Early Warning System does not rely on a single point of data to determine a missile launch against the US. The redundancy in that system required to authenticate a missile launch or a false indication is quadruple in checks. Massive RADARS, Satellite Launch Detection ( Formerly DSP-3 and currently SBIRS Satellites ) and other means of detecting an actual launch are verified before an alert is ever sent out to prevent the mass chaos as portrayed here.
The courthouse shown in LA has many courtrooms, and on any given day they are all in use. Yet despite the massive number of people there, the only ones that end up in the bomb shelter are the people from the one courtroom.
The inmates are the only ones without phones, yet the inmate without seeing the alert or hearing anyone talk about the alert knew how much time there was before the missile was to impact.