After reading this article, I started to question if I should be designing websites taking into account the RGB wheel instead of the RYB.
What wheel should I be using for color selection for website design?
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First off, be careful taking information from sites like the one you linked. It's a marketing site, which means it's trying to get as many views as it can, not necessarily providing great, researched information. The specific article you posted doesn't seem terrible, but it is also mostly just opinion.
To answer your question, you can design using whatever color wheel you feel like using. It really doesn't matter much. Ultimately it will automatically be converted to RGB in order to display it on the screen.
With that being said, the most common color types on the web are hex (a form of RGB), RGB, and HSL likely in that order.
Sorry to ask this, but Why did you use an RYB model in the first place?
An RYB model is a historical model, I must say an outdated one, previously used to understand pigment combinations.
And another thing. An RGB is not a color wheel, it is a color model. A modern color wheel has both, primary light colors and primary pigment colors. Both. Basically has all the color spectrum. Probably not all the gamut of it but all the spectrum.
On a color wheel you chose the color, and then chose the components of it. Either RGB components or some pigment combination.
That pretty much is my response. There is no reason you should use RYB.