Art by hiccuppop on Tumblr
I couldn't find 4/4 SBI as dragons, so you get just Technodragon.
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So, Tommy is just a regular peasant of the Antarctic Empire, right? False. He's extremely poor and homeless and orphaned and he has to steal just to survive. He lives on the edge of the empire, where the other poorer peasants live, near the snowy forest. The previously mentioned forest also houses a thunder (yes, that's what a group of dragons is called) of three ice dragons that the empire have called the Sleepy Boys. They often raid the empire and steal treasure and livestock, often killing a few people just cause.
One way or another, he encounters one of them (preferably Wilbur). Maybe he gets lost and stumbles upon their cave while looking for shelter, maybe he finds one of them injured and nurses them back to health. I don't think that he would look for them to slay them, because 1: he's just a random homeless peasant, the empire isn't going to force him to slay three of the most powerful dragons ever, and 2: even Tommy isn't stupid enough to think he could take on three gigantic ice-breathing lizards. Either way, he encounters one of the Sleepy Boys and catches the thunder's attention. Maybe it's his golden hair and gleaming sapphire eyes that draw them in at first, but then they're drawn in closer by his endearing personality, and before they know it, they're all attached and think of him as their little hatchling/clutchmate.
I think they'd keep an eye on him somehow before taking him, they'd stalk him as he goes around town. If his first contact with them was nursing one of them back to health, then they would probably try and get closer to him and talk to him, starting with thanking him and progressing to having full conversations.
Once they can't wait any longer, they try and convince him to come with them, to join their thunder. Tommy refuses, of course. If they've just been stalking him, then he says no because they're clearly dangerous and are certainly conspiring to eat him. If he's been talking to him, then it's probably because they're dragons and he doesn't trust them yet. If they've never had contact with him before the confrontation, he tries to run back to his village and warn the empire about them, but is inevitably caught by the faster and stronger reptiles. If they've been talking, they probably act like it's all fine, but they're just waiting until he goes to bed so they can kidnap him and take him away. Either way, he wakes up the next day in a soft nest, covered in treasure and wrapped up in soft blankets in the SBI's cave.
Tommy is obviously very scared and angry, but the three dragons are very patient. They know he's been brainwashed by all the stories about kidnapped princesses and burning villages he's been spoon-fed by the empire, and they have all the time in the world to wait now that their hatchling/clutchmate is finally here with them, safe in the nest. It's only a matter of time before he accepts his new family.
If you want to make it more interesting, you could make it like the vampire dark SBI fics where Tommy gets turned, but into a dragon. It would certainly not be good for Tommy, growing new body parts and scales and horns would definitely hurt like Hell. It would be good for the SBI though, as it would make Tommy more dependent on the thunder and impossible for him to go back to the humans.