On the contrary, follow specifically does refer to a continuing future action.

"Follow that cab!" doesn't mean just for one block. You expect the driver will follow that cab until you tell him to stop following it.

To agree with you, however, the cab being followed need not be aware of your continued future action. They can speed up, slow down, stop, U-turn, do whatever they would do if you weren't following them. To your point, "follow" is not "interactive". It's active for you, passive for the one being followed.

It's therefore the perfect word for Twitter's button.