You don't "have" to do any work, unless it's written into your contract. But if you want your book to be a success, you'll want to work on promoting it. These days, even the best and biggest publishers expect an author to put a lot of their own time and effort into book promotion --gone are the days when you could relax, put your feet up, and expect the publisher to do all the work (if those days ever even existed!). If you have an agent, they'll help you do things like book interviews and speaking engagements. If you don't have an agent, you'll want to be in close contact with your publisher's publicity department.
As far as actual writing work, publishers can and do sometimes ask for substantial revisions. But again, this is different now than it used to be. At one time, publishers were willing to spend a lot of time and effort whipping a promising manuscript (and its author) into shape. Now, publishers want a manuscript to be basically print-ready before they ever see it. So there are fewer revisions after the contract, but a higher bar to surmount to even get to the contract stage.