Both of them were certain. They agree on two keys out of twelve.
In 1911 the musicologist Sabaneyev published Scriabin's table of which colour belonged to which key, and set Rimsky-Korsakov's beside it. Two composers, both famous, both sure, both describing the same twelve keys. They match on D and E. On C, one says red and the other says white.
This is not an attempt to settle which colour a key is. There is no such fact waiting to be found, and the page would be worse if it pretended otherwise.
What is worth looking at is the association itself. We form them constantly — some learned, some perceived, some built on purpose out of a theory — and from the inside they feel identical. A thing simply is that colour, or that shape, or that sound, and the certainty arrives before any reason for it does. That is not a defect in Scriabin or in Rimsky-Korsakov. It is the part of being a creature that makes any of this possible at all.
The useful question is not whether an association is real. It is whether it is load-bearing: whether it survives contact with other people well enough to build something on. Some do. Every audio effect has a visual twin is six that did, and a working mixer made from two of them. Pitch and colour is not among them — which is why that mixer uses colour only to mark which channel you are dragging, and claims nothing by it. This page is what the other end looks like.
Who these two are
Why they are in this order
The circle of fifths, because that is the order Sabaneyev printed them in, and because for Scriabin the order is the claim. Read chromatically his list looks arbitrary. Read in fifths it is a spectrum, which is exactly what he said he did to build it.
Rimsky-Korsakov's list does not resolve that way in either order. His white, his darkish, his gloomy dark blue with steel shine — those are not positions on a spectrum. They are what something looked like to him.
What this cannot tell you
Sources