Are the tags always refreshed?

Yes and no. This answer might seem confusing, but it really depends on caching.

A cached website is always fast. Caching is enabled on the server side, and WordPress websites often have additional caching plugins installed. Also, well-developed WordPress themes feature caching capabilities. So, yes, your website can be very fast with effective caching.

The tag cloud widget will display random tags on each page, without a doubt. Then, these tags will also get cached. This means you won’t see new tags every time you refresh the page in your browser. This is standard behaviour.

Tags will be refreshed either when you clear your website’s cache or when the cache expires.

It’s one thing to enjoy seeing tags reload every time you refresh the page; it’s another to have a plugin that doesn’t compromise your website’s performance and serves random tags properly.