I dealt with a similar problem recently on a client site using Cloudflare, WP Rocket, and a plugin that loads a mobile-specific theme.
In my client’s case, the problem was not at Cloudflare. Indeed, the problem could not have been at Cloudflare… since Cloudflare doesn’t cache HTML by default (unless you’ve specifically configured it to do so with “Page Rules”)… and the client’s desktop and mobile sites used different themes and were very different (not the typical “responsive” design wherein the same HTML is served with different styles).
While Cloudflare could be the cause in @vintageman’s case, it may be worth looking at other possible causes as well, especially as Cloudflare folks seem “confused” by this ??
Here’s what I suspect could be going on:
The “Newspaper” theme loads a special mobile theme on mobile devices, complete with its own mobile-only template files. So the actual HTML served to desktop devices is totally different from what’s served to mobile devices. This is explained by the theme’s developer here: https://tagdiv.com/mobile-theme-automatic-optimization-for-mobile-newspaper-theme/
Just as with my client’s case where a plugin loaded a different mobile-only theme, this makes caching tricky: the caching plugin needs to know what this “mobile-only” theme is doing so it can generate separate cache files for desktop and mobile devices.
In the above link, the theme’s author specifically mentions that “the Mobile Theme works fine with WP Super Cache plugin”, and provides specific configuration instructions here:
https://forum.tagdiv.com/cache-plugin-install-and-configure/
Other caching plugins may require specific configurations to prevent the sort of problem you’re experiencing. WP Rocket’s documentation linked below provides some hints on this. In my client’s case, the “Separate cache files for mobile device” feature solved the problem:
https://docs.wp-rocket.me/article/708-mobile-caching
If the above links don’t solve your problem, I’ll advise you to contact both the WP Rocket plugin and the Newspaper theme developers for help. As these are both commercial products, there’s not much more we can do to help you here.
Good luck!