The Time Vessel Association began in the Nara period during a time when Master Tengen first began to spread Japanese Buddhism. They preached what would become the foundation for jujutsu sorcerers. However the worlds of jujutsu and religion don't agree and the Time Vessel Association was born from that disparity. The group maintained its monotheistic ideals all the way until the modern age.
By 2006, the Time Vessel Association was a wealthy religious group that operates in the underbelly of the jujutsu world. They worshipped Master Tengen as their sovereign deity referred to as the "Star" (星 Hoshi?), making the organization officially known as the Star Religious Group (盤星教 Bansei Kyō?) to the public, a congregation of non-curse user's that can't be targeted by jujutsu sorcerers. Follows of the faith were called Children of the Star (星の子 Hoshi no Ko?).
As Master Tegen's evolution approaches, the threat of an impure merger is cast on the Time Vessel Association. The Star Religious Group sees this as taboo because they worship a pure Master Tengen. If Tengen were to merge with the Star Plasma Vessel, it would soil their purity and dissolve the association.
Without the power to fight it, the organization uses their resources to enlist the Sorcerer Killer: Toji Zenin. They offer to pay him thirty-million yen for the assassination of the Star Plasma Vessel: Riko Amanai, which he accepts. Despite not yet receiving the funds, Toji uses the money put a bounty on Riko's head on a website for curse users.
The association warns Toji that if the bounty is claimed, he won't get any money. However, he's using the bounty to wear down the special grade sorcerers protecting the vessel, Satoru Gojo and Suguru Geto The Star Plasma Vessel's escort team is able to repel the first wave of curse users. A non-curse user member of the association kidnaps the vessel's caretaker Misato Kuroi.
Toji suggests that they kill her but they decide to let their enemies rescue her to create a false sense of security. This results in the escort team traveling to Okinawa to rescue her using a private jet, something Toji and the representative who hired him find hilarious.
The Sorcerer Killer is eventually able to defeat the escort team and successfully assassinates the Star Plasma Vessel. He brings Riko's corpse back to the House of the Children of the Star as proof of his success and is paid extra for his troubles. However, Toji is defeated shortly after by a restored and fully awakened Satoru Gojo, who takes back Riko's body.
Satoru and Suguru are only met with followers of the faith. The ones in charge connected with the jujutsu world fled, but the association was forced to disband due to existing problems in addition to being unable to excuse their actions against Jujutsu High.
Even after the Star Religious Group disbanded, the remnants remained in association with other likeminded groups. After Suguru Geto becomes a curse user, he assumes control of all of them during a large congregation that included directors, representatives, and the chairmen. Initially, there are many voices of opposition against Suguru until he murders Sonoda on stage, forcing all the non-sorcerers to obey him.