[Lucifer didn't make him promise not to kill anyone. What a colossal mistake.
All the same, Sebastian isn't stupid. Young and impulsive and hedonistic, but not stupid. He expects Lucifer not to trust him; expects him to keep an eye on what he's doing and what he chooses to pursue... at least initially. So Sebastian will just be very good, initially, and go have some unfortunate animal instead of a human. He's hungry enough that one measly soul won't fill him up completely - there's plenty of time to have more later, once he's sure he's been left alone. And souls are souls, whether they're delicious or passable, aren't they?
Sebastian doesn't make it to "later", however. He makes it to the forest, and to an unlucky deer, and to his claws burrowed deep into its flesh and his shadows enveloping and muffling the animal's pathetic cries.
That's when the event ends and Sebastian is returned to his normal appearance: with the deer's carcass on the ground before him, its blood on his hands and on his (usual, right-sized) clothes, and the taste of its subpar, disposable soul in his mouth.]