Reign and the others didn't need much time to set up the speakers around the city, nor did they need a lot of time to gather people outside their homes so that they would listen to what they were about to say.
The speakers were automatically placed by the system, so truthfully, Reign and the others had nothing to do but wait for the people to gather around. Of course, they didn't just wait.
They were meeting the many groups of the city that had risen against the Butcher or were neutral and did their best to help out the citizens as much as they could. It was from them that they learned of the hundreds of people who were outside of the city.
Those people had left and made their own little territories outside. Even though it wasn't that safe, they were free, the Butcher and his gangs didn't know about them and they could do whatever they wished to do.