Here's one example from Girls' Generation. When they introduce themselves, they always count forward — 하나 , 둘, 셋, we are Girls' Generation. But Yu Ri Kwon counts backwards at 13:57 — 삼, 이 , 일.
They don’t know, too.
As to why no one answers this question asked a week ago, it’s because it’s something native speakers would find natural but don’t know the exact rules for that.
Don’t sweat it though.
It’s just a tendency, if not preference, however; you can use both native and Sino–numbers to count forwards or backwards if that doesn’t involve units (“if you don’t say units when counting”). Both sound good.
This doesn’t quite answer your question, please accept another one that’s more complete.