Document how browscap works with page caching

I installed this module on my project and it works just fine to detect the current browser using browscap_get_browser() which I am using to apply browser specific stylesheets. However, once that information is retrieved, it is saved in drupal cache and then if I visit the website in some other browser, it still has the stylsheets from the other broswer and I need to clear off drupal cache to get the correct stylesheets for current browser. Is there a way to handle this situation apart from setting to not cache pages in Performace. Any help in this matter will be helpful.

Thanks,
Sumit