For new visitors it's not an issue, for returning ones it might or might not appear like that. It's very hard to tell, because in this case the caching is on the client side.
There is an auto generated query string added automatically after the search CSS files each time after the settings are saved, it kind of forces the browsers to re-download the files. But of course this is not a permanent solution, as if there is a cache plugin also installed, then it often minifies + aggregates the site stylesheet files and manage the query strings themselves. Plus if there is a 3rd party cache layer, like cloudflare used as well, then it's even more difficult than that, as it caches the files as well, often with the query strings.
Not to mention that browsers tend to ignore the query strings if they want to, so from our perspective there is no reliable solution to manage browser caching unfortunately. I myself struggle a lot when I push an update to the demo sites, because I use W3TC + Cloudflare + Varnish cache for the best performance, but it makes cache clearing a nightmare.Best,
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