Ok, so do The Reckoning, then you can get this triumph and then you can start the Allegiance quest. I recommend that you make sure that your Pursuits bounty isn't full, as there has been issues when the bounty will drop but it won't go in player's inventories.
Just did a prime match and no weak synth
Do you have the User Testing quest? If so, you may need to complete that first.
They're not full