Having just refreshed myself on Tsushima (from the book, Kaigun) I was surprised to read that it's estimated that the Russians landed at least as may heavy shells on the Japanese battleships as the Japanese landed on the Russian battleships--in other words Russian gunnery was not as bad a is commonly held. The big difference was the Japanese ordinance, with Japanese shells not concerned so much with penetrating armor but in destroying superstructures and igniting conflagrations.
Is this difference in ordinance modeled in the game?
The Japanese use HE exclusively in calibres < 8" and significant quantities of it when shooting with guns >= 8". HE is more likely to cause fires in the game and as I recall Japanese (and British) HE hits have a slightly better chance of starting fires than others due to the higher flame temperature of the picric acid based high explosive fillings compared with TNT based explosives used by other naval powers.
So, why wasn't picric acid the international shell filling of choice? Compared to TNT picric acid-based compounds (Shimose in Japan and Lyddite in Britain) had many downsides that were only really revealed during the Great War.
So the short answer is that yes, this is modelled in SAI-RJW but the effects have not been exaggerated as there are many factors involved in whether a shipboard conflagration occurs or not.
In the gun vs. armour competition of the era, there is plenty of evidence that during the RJW armour was ascendant, something much less true a decade later as AP ammunition design, materials and quality improved.