Hello, I just completed the Pit of Heresy solo and did not receive the triumph Usurper. It was also my first Pit of Heresy completion overall. I got the triumph for completing the Pit of Heresy, but did not get the Usurper triumph even though no one joined my fireteam throughout the activity. I completed the activity through the game via Steam.
Did you complete the run in one go or did you return to orbit at any point? Unlike solo (non-flawless) for Shattered Throne, for Pit of Heresy solo triumph, you need to complete it in a single session.