Leonidas only had 300 Spartans to begin with. He never, at any point, sent Spartans home from Thermopylae. He sent Greeks from other city-states. He arrived with 300 Spartans, 300 Spartans stayed, and 300 Spartans died.
They didn't stay to buy time for Sparta to evacuate. Sparta never evacuated. Leondias left approx. 9,000 hoplites to defend Sparta should it come to that. They would NEVER have left Sparta. They would have relished the chance to die in her defence. There is evidence the 9,000 who stayed were entirely unsatisfied at having been left behind. The idea of Sparta evacuating is absurd. They would have welcomed a battle like you and I would welcome a steak dinner. There is even evidence that the women were trained in a warrior cult much similar to the men, and there are documented accounts of Spartans princesses leading all-female phalanxes into battle.
Leonidas bought time for Athens to evacuate, not Sparta. Themistocles, after his stunning naval victory, headed to Athens and evacuated her citizens, moving them temporarily to Salamis. Xerxes reached Athens, and found her empty save a few preists and priestesses who stayed at the Parthenon. He burned an empty Athens to the ground, not Sparta.
Sorry I missed this initially. I highly recommend you do some more intensive research