When it comes to these sorts of Urgent Quests, it is more efficient to stick with the entire MPA and farm off of the enemies, as clearing the quest merely means you have to restart the quest, since enemies will no longer spawn for you. Any sort of reward for clearing the Urgent Quest in these types of missions is peanuts compared to sticking around and grinding on the oodles of monsters that spawn. Pop a tri-boost, RDR boost, and an Exp boost, and get to killing. The more people in a condensed group means more spawns in a small area. More spawns in a small area means more shots at PSE Triggers. More shots at PSE triggers means a greater chance at a PSE Burst. And when a PSE Burst happens in a large group of players, there is a FLOOD of enemies. Chain your PBs, and watch the exp roll in. The aim for these quests are to get exp, which typically comes from the monsters, who give a lot more exp than normal, compared to exploration quests. Yes, you want to trigger E-trials as they happen, and clear them, though clearing them will make all the remaining nearby monsters retreat and despawn, though if your MPA is efficient enough, they'll all get killed before they can.
All in all, focus on killing mobs in these UQs. That's where the exp is.