If you're running a company, your team is definitely doing one of these things; designing a feature, coding a feature, fixing bugs or selling a feature to your clients in a broad sense. You then have a priority on what to build/fix and when to build/fix, often decided by the person in charge. Then there's a deadline (weekly, fortnightly or monthly); which people meet (which is good) or do not meet (in which case you do a retrospective of what went wrong and make sure it never happens again). And whenever something is ready you ship your code and you don't let it rust in your staging branch or staging machines, you want it to you reach your users, if you're not doing that regularly, then you might as well shut shop and call it a day.
Waterfall model is where your workflow moves from top to bottom, requirement analysis and design, writing code, testing and delivery. Whilst often criticised for the lack of of inflexibility, all the other models are variants of the waterfall model with more flexibility. DevOps culture is mainly about getting code to your users as soon as they're tested and ready. So, when your testers sign it off, you ship it. So, I don't see why DevOps culture won't go hand in hand with Waterfall, unless I have gotten the definitions of Waterfall and DevOps Culture wrong.