Customizer Appearance Issue

It sounds like it could be a server side caching issue. Assuming the refresh you mention is to your browser, this would not necessarily fix the issue.

Shared hosting servers can have various tiers of server side caching and/or services like Cloudflare that can cause issues like you describe. Without knowing the specifics of your hosting environment its hard to rule out or advise a fix.

I’d suggest giving your shared hosting support line a call and asking what caching might be running, and seeing if you can flush it our turn it off to rule it out as the problem.