I was able to find a workaround for myself, but it did require shipping a new build with an updated .icon file, and I still consider there to be a bug on Apple's side. I don't know much about the SVG file format or how my file got this way, but it turns out the SVG embedded in my .icon file had two different colors in it, with the unwanted one in an inline style attribute. This is visible by right-clicking the .icon file in Finder, selecting Show Package Contents, browsing to the Assets folder, and opening the SVG in a text editor: <path fill="#ffffff" ... style="display:inline;fill:#800000;stroke-width:0.273;stroke-dasharray:none" /> In Icon Composer, with the "Automatic" fill mode selected, the red #800000 color isn't shown—it shows white. But at some point in the last couple weeks, there seemed to be an unexpected change in the rendering and caching of this SVG so that the style attribute takes precedence web-side, even though Icon Composer doesn't display it that way. So by changing Icon Composer's fill mode explicitly to the solid color I want, I seem to now get the result I want (after shipping a build with this updated icon file).

Thanks, @DTS Engineer. To be clear, the icon is not an image file (CMYK or otherwise). The icon was built using Icon Composer and imported into the project following these instructions. My main concern is that the icon in the App Store has changed without me taking any action. Since my initial post, the iOS App Store product page has now changed too. At 1:37 AM (first screenshot), it showed the expected icon. At 12:25 PM (second screenshot), the same product page now shows the modified icon. It's the exact same app version and build—not touched in two months. That makes this look less like a local previewing issue and more like an Apple-side issue in the pipeline that processes .icon files and caches the result.