They have clearly existed for a considerable time, since they knew who Mathias was, whilst Richard Croft was still alive, even recruiting his research assistant, Danny, into their ranks. They possibly attempted, to help the Solarii, but ended up trapped on Yamatai as well,
The group saw Mathias as a divine man who would help to save the world, and the only one who truly understood Himiko.
After the death of Mathias, they sought a way to resurrect him, and saw that an ancient prophecy seemed to be the way to do it. involving four calamities, four guardians, and four relics, which were parts of a house. Little did they know, the prophecy was being set into motion by one of their former members, Danny Who was intent on stopping them from resurrecting Himiko.
Matsu sent his own daughters to retrieve two of the relics needed, one which was in the possession, of Professor Cahalane, and the other which was in the possession of Lara Croft. One killed Cahalne to retrieve the Relic, and the other headed to Lara's flat, which she ransacked, but couldn't find the relic, though she carried out another task, and kidnapped Samantha Nishimura, to use as leverage against Lara Croft, who they believed to be key to reviving Mathias. They took Sam to Yamatai, knowing that Lara would follow. When she arrived, Lara was captured, but before she could be sacrificed, Jonah and Reyes came and interrupted the ceremony. Matsu attempts to kill Lara, but he is attacked by Sam, who unintentionally completed the ritual, allowing Mathias to come back, though his resurrection was short lived, as Lara destroyed Natsu's body with a grenade.
Danny attempted to stop the group from being able to ever be resurrected, by killing his last 'guardian', Lara. Lara killed him in self defense, and the group likely fell apart after the failed attempt at Mathias' resurrection, and the deaths of many of their members.