The two acts were brought in to replace trio Rough Copy, who had to be dropped from the show because of VISA issues.
Times Red feature Staz Nair, Scott Ritchie and Luke White, and the Essex collective were one of the most popular acts at the first auditions.
Triple J have been renamed Union J because they have added an extra member - George Shelley - since they were originally axed from Boot Camp.
Louis Walsh and Sharon Osbourne selected the three Groups to take through to the Live Shows during a trip to Vegas.
The other acts hoping to progress are North London trio Mitsotu, beatboxers Duke, hip-hop pairing MK1 and stage school boyband GMD3.
The X Factor Judges Houses shows will air this Saturday and Sunday (September 29-30).
X Factor - The Original Top 24: