Hi @Nina118
I'm very far from an expert at all things IT, but I highly suspect that this is happening for you alone, particularly if you are using the same browser as you use when using airbnb.
I think you will find that the combination of browsing history, cookies and same IP address, combine so that when you google as a "stranger" the internet pixies actually do know it's you - you're not searching incognito you're automatically being recognised and logged in as the airbnb owner.
IF you try a google search from a completely different computer and/or or use a different browser and/or clear your cookies and browsing history and then try again and it's STILL happening there may be a problem.
As I say I'm not internet savvy and dont' have all the appropriate jargon, but I think I've communicated the essence.
Hope this helps.
Somebody more skilled will probably be along shortly to help
Regards