Good question, LTS!

To me, the phrase "new old fashioned way" implies reviving an old custom, but doing it in a new way. The new way must mean rock 'n' roll. That implies that, before that, people used to dance around the tree, but it wasn't the rock 'n' roll type of dancing.

However, I'm not aware of any custom of dancing around a Christmas tree. In fact, in my experience, Christmas trees are always placed against a wall, so it would be impossible to dance around it. Who has a house big enough to put the tree in the middle of a room, so people can dance around it? Maybe I'm being too literal.

The phrase certainly IS mysterious, and I never thought about it until you mentioned it.