In reply to A-Tank
So far the Vale Branch is the only one that's complete (I imagine that there's a branch in each Kingdom, but the only one aside from Vale with any named or designed members is the Vacuo Branch, which is run by Nephrite parents, Pyrite and Tourmaline). Each branch of the SIN-dicate has two teams, the main team that does the actual stealing, and the recon team that gathers as much information on a target prior to the main team going in for their missions. The Vale branch's main team is led by Nephrite Sin, and his second in command is his childhood friend, Modry Hrich. The team mechanic is Ilēkṭrīka Phlēra, the person in charge of keeping mission uniforms in good condition is Azurite Colpa, and the muscle of the group is Mávros Amartía. Other members of the main team include Nephrite's best bud Nis (last name not yet determined), Nis's younger sister Kōraru, Tsumi Minto, and Zondigen Eustoma, who Mávros sees as a little brother.
The recon team is led by Cobalt (last name not yet determined, in fact Cobalt might end up being a place holder name), and the second in command is Cygnus Ray (or as I like to call him: worrying group mom). The other members are Nephrite's adopted younger brother Aspen Sin, Regina (last name not yet determined), Nisha Avocet, and an un-named character who's also the team medic. Sorry for that super long winded introduction but if I'm going to cover how they reacted to the fall of Beacon I figured I should introduce who everyone is.
First, I imagine the SIN-dicate headquarters didn't really get hit anywhere near as hard as some of the other parts of Vale did since I imagined SIN-dicate headquarters for the Vale branch was built inside a large warehouse near the coastal border of the city, meaning it's farther away from the large crowds, and isn't as close to the area the grimm are coming from. I can't say for sure how Modry, Nis, Tsumi, Zondigen, Cobalt, Regina, or the medic dude would react since they all belong to my friend who collaborates on the SIN-dicate, but Nephrite would desperately be trying to find each and every one of his team members (assuming they're not all in one place when it starts), because while he's normally a carefree party animal, he sees all of his team mates as honorary family members and probably wouldn't be able to handle it if anything bad happened to any of them.
Ilēkṭrīka is probably the most level headed out of any of my SIN-dicate members, and as soon as the warning goes up about the incoming grimm attack, she immediately goes to grab her weapon. Mávros would be just as level headed as Ilēkṭrīka if not for the fact that he's probably worried out of his mind about making sure Zondigen stays safe. Azurite would probably be trying to stay close to the other SIN-dicate members since he's the only one out of the main team that doesn't really have any combat training. He's picked up on a few basic tactics and maneuvers from watching the others train, but he kinda needs to stay close to the real fighters to stay safe. Kōraru is probably following the same strategy as Azurite and trying her best to stay close to the team, especially her brother. She has combat training, but she's only really good at fighting in areas with lots of walls since she has to rely on her echo-location semblance to know where her opponent is (she's blind), so outdoor fighting isn't particularly good.
Cygnus is in a total panic, desperately trying to think of ways to keep his friends safe. Aspen pretty much instantly goes into combat mode and gets his weapon ready and goes to keep a look out for any grimm headed their way. Nisha would probably also be keeping a pretty level head about the situation, and would get ready to fight in case any grimm head their way, but is also doing her best to help calm the others down (mainly Cygnus, since this dude is probably panicking so much he's probably on the verge of hyperventilating). Overall, I think they'd be a lot calmer than your average citizen since 1. Almost all of them have combat training and experience, and 2. they're aware they're in the closest thing to a safe location they're going to get.