I have been looking at the Leadership feat and there doesn't seem to be anything that says whether you are supposed to pay your cohort. Torchbearer feats description implies that you are supposed to pay your followers under normal circumstances however it doesn't mention anything definitive.
Unlike other hirelings, a torchbearer requires no compensation for her services as long as her employer has this feat; the opportunity to train under a hardened adventurer is reward enough for most torchbearers.
So do you have to pay your cohort/followers or do they just follow you around because of your extreme leadership skills?
No, you don't have to pay your cohort/followers.
The Torchbearer feat mentions paying compensation to other hirelings, but that is meant to refer to deliberately hiring people to provide services, as per the Hirelings, Servants and Services section. The function the Torchbearer ostensibly provides (someone to wave around a light source for you so you can see in a dungeon and keep your hands free) is something which could be traditionally done by simply hiring a lackey.
The Pathfinder Player Companion: Cohorts & Companions supplement specifically clarifies, in its introductory segment under the heading Reasons to Follow, that (emphasis mine):
So no, you are not expected to normally have to pay followers and cohorts, they are able to support themselves. You may need to provide equipment and supplies to your followers if you task them with actually doing something, but their time is essentially free.