“Actually it protects individuals from being tried twice for the same crime.”
It also protects individuals against sentence increases once the sentence is served. Very rarely are sentence increases allowed even with the judge being in error with sentencing. The only exceptions have been when judges have corrected their sentencing errors immediately, before the defendants began serving their sentence. Re-sentencing after time served is where double jeopardy comes into play.
But it does happen. Which means it isn't double jeopardy because it isn't unconstitutional.