I'm traveling to Shanghai on 19-26 December. it is a must to get a down jacket?

Yes, at that time, it may be cold (the lowest temp may drop to 0 degree Celsius and the highest can be 10 degree Celsius). You need to wear down jackets. If you think your jacket is not warm enough, you can take a sweater. The sales lady just wanted to sell her jackets to you, that’s the reason why she said that.