While they are, at first, believed to be working for SERN, it is soon revealed that Rounders work for an organization independent from SERN. Unlike SERN, who carries out the actual research, the Rounders operate in the shadows, carrying out tasks such as assassination in SERN's stead. The Rounders receive orders from FB. Moeka is revealed in episode 12 to be the leader of their assault/retrieval team for the time machine.
Despite their appearance, the Rounders are well-trained professionals, having the ability to infiltrate and overwhelm Akihabara in a matter of hours. Their professionalism is shown through many different ways, most notable of which being their ability to prevent entry to and exit from Akihabara via an unofficial vehicle search and a bomb threat, and following Okabe and rendering him unconscious without being noticed until the very last moment.
FB declares in episode 20 that he "rounded" up the Rounders (who in turn "round" up the lab members) by psychologically profiling shut-ins in the region as potential members: individuals who are so detached from society that he could easily manipulate them according to their emotional needs to work for him. (Shut-ins are a known real-life phenomenon in Japan known as hikikomori .) It is unknown if FB or someone else provided their armament, but either way, their emotional coldness and anti-social personality may be a hint towards their capacity to obediently follow orders with absolute ruthlessness and efficiency.
In the anime, the Rounders wear mask to conceal their face with the exception of Moeka.