Your question has two parts.
A. Which file formats and color modes are required.
B. The process you follow to make those files.
For the first question, as @Scott mentioned, simply go to the website and take a look at the requirements.
Should I design in CYMK and then convert when exporting the PNG.
No. Do not do that.
First of all, always try to design, especially when using vectors (Illustrator, Affinity Design, CorelDraw), in the final color mode you need.
But when illustrating and retouching in Photoshop, you most likely are using RGB on the project. Stay that way, and only convert to CMYK an output file as the last step.
Working a file as CMYK and then exporting to RGB will give you a dull image because you are telling the file that you actually want the RGB file to look as a simulation of a CMYK print.
If the provider requires an RGB file, which is typical on digital prints, it is to have more vibrant colors, so on that case, maintain all your process as RGB.