Well first of all, the Designers should definitely take a look into how React works. And have a basic understanding. As the Designers are doing the HTML and CSS and not the Frontend Dev, they should've some basic technical understanding of how things work.
The cool thing with React is, that you are working in components. And this is also a very important point for the designers (frontendlers), because they need to learn how to design and markup modular components.
So they are basically two ways around this.
Markup all the things. So the designers coding the components, Markup and Styling and hand them over to the frontend devs which are building the react components.
The important part is now, if something changes.
However this is only important if they change markup. Style changes can be made normally in the css file.