Some evocation spells do damage without a saving throw
Other current answers present very valid answers to the sub-questions in this post:
So, if I'm reading this correctly, why not just say that those in the 'pockets' take no damage if there's a save? Why all the extra words?
The answer to this being that many spells not only do damage on a failed save, but also impose a condition (i.e. being prone, restrained, etc.).
Yet no one answered the main question:
When would someone in a Sculpt Spell's 'pocket of safety' take damage?
Consider the 4th level Evocation spell (available to Wizards) Wall of Fire (Emphasis mine):
When the wall appears, each creature within its area must make a Dexterity saving throw. On a failed save, a creature takes 5d8 fire damage, or half as much damage on a successful save.
One side of the wall, selected by you when you cast this spell, deals 5d8 fire damage to each creature that ends its turn within 10 feet of that side or inside the wall. A creature takes the same damage when it enters the wall for the first time on a turn or ends its turn there. The other side of the wall deals no damage.
An Evocation Wizard using Sculpt Spell to exclude his allies cannot protect them from the second source of damage, which targets anyone that is within 10 feet of one side of the wall at the end of its turn, or goes through the wall. You can then see that someone in a Sculpt Spell's 'pocket of safety' can take damage in that situation.
There is also the ambiguous case of having a Dexterity saving throw on a paralyzed creature in a Sculpt Spell's pocket of safety.