This is where the GM adjudication comes in. The party has a bunch of "hirelings" that are paid to guard the camp, take care of the horses, and haul the stuff back to town when the party gets it out of the dungeon. The party decides that it would be a good idea if some or all of the hirelings would go into the dungeon. OK, why is that?
A. The party wants some extra help. That is, they want the "hirelings" to act more like "henchman". You adjudication is all about what's in it for the hirelings. This is a potential promotion--more pay, but also more risk. Some might be inclined to take it. Others say no way. Even the ones that are inclined to take it (reaction roll) will have somewhat different ideas of what it means. One guy is planning to risk it one time, and if he makes it out, take his share of the gold and open a general store back in the village. Another guy sees this as his gateway to fame, his big chance. He'll expect to be a henchman from now on.
B. The party is being pursued in the wilderness. They've been to this dungeon before. They think the best chance of survival is to hole up in the dungeon in a spot they know to fight off the pursuit. Or maybe they know a second exit that they can use to lose the pursuit. Of course they want the "hirelings" to go into the "dungeon". They might need to do a little fast talking, but it is in the hirelings best interest to go. Assuming that all works, when they get back to home base again, some extra pay for the hirelings is probably in order to keep morale up. Not so much because they explicitly went into the dungeon but because of what it represents: The jaunt got risky enough that going into the dungeon was the best option. On the other hand, assuming it works, the thrill might be enough for some of the hirelings. Adjudicate it based on how you see them.
The henchman and hireling rules are put into place to give you a starting place to handle some of the most common adjudication needs for having retainers. They are not meant to replace your adjudication.