Mobble and Caching problems

So, does it mean that the $_SERVER[‘HTTP_USER_AGENT’] is cached, and then the info served to me comes from some other user device?

Not quite. Most cache solutions provide a full page cache of some sort and do not vary by user agent. So when visitor A comes along, they are served an uncached page and the page is cached according to their user agent. Then visitor B comes along and gets served the same page that A got as it has now been cached.

In your opinion, what kind of cache setting should be changed to avoid caching of that information and so make mobble work properly?

You would need to tell make your caching plugin aware of the same user agents as those used by mobble. So if you are using a function like is_android(), you will need to work out which user agent that matches in mobile_detect.php and make your plugin vary its cache based on that same user agent. Things should then work as expected as the plugin will create a new cache for each user agent type.