On demo instance (M5.5.2) I can reproduce this issue. Follow these steps:

1. Opening https://demopublic.magnolia-cms.com/ in browser 1 (e.g. Firefox)
2. Choose travel type 'cultural'
3. Opening https://demoauthor.magnolia-cms.com/.magnolia/admincentral#app:jcr-browser:browser;/travel:treeview: and publish a node for cache flush on public instance
4. Reload https://demopublic.magnolia-cms.com/ in browser 1
   1. cultured tours variant will be shown, because of your tourType cookie
5. Opening https://demopublic.magnolia-cms.com/ in browser 2 (e.g. Chrome)
   1. cultured tours variant will be shown, BUG there is no tourType cookie
      
   2. with additional parameter the right original variant is displayed (e.g. https://demopublic.magnolia-cms.com/?test=1)
      

Another way to reproduce (from ahietala):

1. Wait until the live demo resets. On the hour (:00) or half hour (:30).
2. On the public instance, request the travel home page as a Chinese visitor.
    https://demopublic.magnolia-cms.com/travel?previewCountry=cn 
3. Request the same page for an anonymous visitor.
   https://demopublic.magnolia-cms.com/travel
4. Problem: Magnolia cached the personalized content variant (Temples of the Orient) and keeps serving it to a non-personalized visitor. Anonymous visitor should get the original content (Hut to Hut in the Swiss Alps).