Chose Venture company this week. Did the side gig quests and they all rewarded 200 rep each for Bilgewater. The world quests gives rep for Venture Co. but does not give 50% bonus from “Sign of the Emissary”.
Side gigs are intended to give rep for the cartels you run them for, hence the name. They aren’t tied to the one you choose for the week in any way; they simply rotate between one zone and the other each week (Zuldazar and Ringing Deeps).
The issue is the reward in the quest show the reputation of the faction you chose that week - in my case, Blackwater Cartel Commendation - but when completing it shows Venture Company in the log.
Edit: I noticed one of them was Venture Co. and the others Blackwater.