Sadly, this is "normal" behaviour. The tabs themselves cannot see each other, they run separately and unaware of each other. As others have mentioned, the effect could be the result of cookies installed on your computer which can let other websites know what you have been searching for. Keep in mind, this would require co-operation between websites. Some random website cannot read the cookie of another website, there has to be some kind of agreement between sites that allow them to access each others cookies and share information.
Turning off cookies can help curb some of this behaviour but that usually comes with a hefty price tag, no more saved passwords/settings for websites, it'll just make sites more difficult to use and generally a nuisance. You'll end up turning cookies back on anyway for the convenience.
In my opinion, that's probably not what's going on, cookies are just too pedestrian, they can very easily be cleared and data on your habits is lost. Your habits and likes are the money maker, companies like google don't want to risk losing that information.
I think it's more likely that the advertisement is based on profiles built based on IP address. If say you are using google to search but don't have a google account, they can still track your interests based on the sites you click on in a google search and your search terms. It's not as accurate but still generally useful. If you have a google account, then even better for them to build a better profile.
So when you do a search for cars, the search engine knows that your IP address is interested in cars. Then when you visit a new site that is likely running adds from google, the adds will be based on whatever information google has tied with your IP address, in this case, advertisements for cars.