Yes, and nothing needs excluding. Every visitor is served the same HTML; their own choice is read from their browser and applied before the page is painted. Usage statistics count presses on cached pages too, however old the cached copy is.
A cached page does carry your settings, though: the starting mode, the dark hours, the screen sizes and the button. Saving a change visitors would see asks your page cache to empty, so the next page is drawn with it. So does switching the plugin off, at once, and the first request after an update, or after switching the plugin back on, that is not answered from the cache. That covers NimbleCache, WP Rocket, WP Super Cache, W3 Total Cache, LiteSpeed Cache, WP Fastest Cache, SiteGround Speed Optimizer, Breeze, WP-Optimize, WP Engine and Cloudflare's own plugin. A cache the plugin cannot ask, such as your host's own or a CDN, keeps its pages until they expire, so empty it after changing a setting.
The one exception is a schedule saved on the Display Rules screen before version 1.2.14, which is decided on the server. The screen shows it with a note; set it back to Always and use General → Automatic Switching for dark hours instead.
Still stuck? Ask the developers who wrote it. We aim to reply within one business day.
Dark Mode
Give your site a dark mode your readers can switch on — one that reads properly on every page, without you restyling anything.
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