How do the monsters interact with humans on the surface?
(Due to previous conversation, I assume this means AuraFell!)
Well, things go...not so good at first.
It would have been easy to hide Aura powers from the humans, since they're so much about manipulation. But Asgore (Dad) is not an unkind monster, and he believed it wasn't justifiable. Alphys and some surface scientists came up with containment units that can suppress Auras, until there's enough evaluations and data to suggest the boss monsters are safe to be released into the world. They're held there, kind of like an SCP Foundation thing, for at minimum 6 months. Monsters without Aura were released after only a month of evaluations, into protected communities with provided support programs.
Mock and Terror are likely the first ones out. Good behavior and Frisk vouches for them, of course. They would have gotten Asgore out, but he insisted on staying in containment until they build a mobile suppression device because he's so worried about his power.
Mock and Terror are assigned some "handlers" that are, hmm, not immune to their auras, but like resistant? I would assume they have some sort of devices equipped to protect them. They follow them around and live with them for the first few years to make sure everything is on the up and up. A lot of humans raised a fuss about that being an invasion of freedoms, but the brothers didn't really mind. Their good behavior gets the rest of the Boss Monsters released slowly, and eventually a device for suppression is made, a bracelet. It's a choice to wear it, but if they don't then they need to have a handler. Asgore naturally chooses to wear it immediately.
Mock becomes an ambassador against his will, but it's better than Terror doing it. They run a few experiments to see if he can record his effect, for science. It's effect is reduced by a lot on record but they find it still lulls babies, so he makes a recording of his lullabies and its used widely once they discover there are no negative effects and it can't coax them to sleep longer than their bodies need or if they aren't tired already.
Terror gets a job as a therapist after a while, working with extremely traumatized youth. It's a little controversial, but nobody can deny he gets the job done. He requires written consent in triplicate on three different sessions before he'll modify a memory, and he has a clause where he can reverse it. He rarely does it, though, since he's actually a very good therapist.