"pull it on" refers to the action of putting on an item of clothing, so in this sentence, it is meaning the common/familiar actions we are all used to doing regularly.
As Gary said "pull on it" has a different meaning, it would refer to the action of using force to move something.
I would also say that, in my opinion, "to pull on a cigarette" is not a common expression but rather the following verbs would be better used:
--> "to drag on a cigarette / to take a drag on a cigarette"
--> "to puff on a cigarette / to take a puff on a cigarette"
--> "to inhale the smoke from a cigarette" (this one is very formal and almost scientific though)