I recently won a couple KOMs during some rides in London and Watopia. In London, I did not place first, but gained first place by attrition, and my jersey changed to polka dots (I think it was on Keith Hill, but not certain). In Watopia, I placed first on the Epic KOM, Reverse Epic KOM, and Volcano KOM. The KOM standings showed me as first place, and I got the little jersey icon next to my name in the nearby rider list, but the jersey I was wearing did not change, not even briefly (and I waited until I was outside of any zones where it might revert to my normal jersey).
Here are a couple screen shots to show what I mean: