I am fairly new to PHP (about 8 months). I am building a web app, which is almost ready for beta. I am only now starting to think about what I would need to do to make a mob
REST is more of a design ideology than a language framework, so NO you don't NEED to use any framework. However there is no advantage in reinventing the wheel (Sure some disadvantages are there like security, structure etc.).
If you want to avoid mayhem of MVC (which is not required specification of a REST architecture) you can use any PHP mico-framework (Slim, Lumen etc) they are really quick to learn and implement and allow PHP developer to write route based app (similar to those of MEAN and Express) saving a lot in time.
Most of these frameworks comes with an MVC as well but if you don't want to give a CMS for the API, MR (Model-Routes) is good enough (and practically the best) for all REST needs.
Since the dawn of angular like frameworks which allows your website to communicate with sever like any other API easily, I think even the CMS should access the API like any other app just with elevated rights or specific end-poin