The Primus is believed to be extremely orthodox, ordering punishments for kett who deviate from social norms and traditions. She is also concerned over the missions to investigate Remnant technology since they intervene with military exercises and recon missions. While the Primus expressed her "concerns" to Archon about the latter's obsession with Remnant, she'd not readily go open with her dissent about the direction Archon took with the Heleus Cluster campaign. However, that doesn't stop the Primus from gathering her own faction, spreading her side's propaganda against the Archon, even gone as far as to solicit the Pathfinder, to engineer the Archon's downfall.
Ryder would first encounter the schism on Elaaden, which would eventually led to a vid-com with the Primus on Eos, where she reveals herself "as a traitor" to the Archon. She believes that Archon's obsession with the Remnant derails their cause and incites chaos. Furthermore, she wants Archon gone and thinks his quest for Meridian is for his own ambition - through various audio logs, the Primus expressed that the kett could and would conquer the Heleus Cluster without the Remnant technology anyway, thus Archon's obsession with the Remnant technology could only mean that the Archon's ultimate goal is to turn against the Kett Empire for his own ends.
In the vid-com, the Primus would propose a deal: in exchange for killing the Archon, she'd provide Ryder the kill code for the Archon's ship, which during the final mission Ryder could use and drastically weaken the kett opposition encountered.
With or without taking up the deal, the Primus would tell Ryder that they'd not speak again.
After the Archon is killed, Primus becomes de facto leader of the kett in Heleus Cluster.