There's no such thing in SC. Don't make it a story.
There may be cases that individual parents may like to send, say, x'mas gifts to teachers, that's individual's mentailty. Like some people loves to buy X'mas gifts for friends.
Such cases may exist but it's not a trend. Not to mention a "must".
Sometimes, some parents would prepare some little gifts for thier children's classmates on their kids' birthday or x'mas, just to make children happy and for sharing purpose. This is a culture, a kind of kindness... I don't see any "requests" from teachers! We've never sent "luxurious" to school, my kid is loved by the teachers, even the "washroom aunties"!