When I refresh a single page oon AB it contacts the following sites....
googlesyndication.com
gravatar.com
facebook.com
addthis.com
google-analytics.com
fbcdn.net
doubleclick.net
adsafeprotected.com
ctasnet.com
switchadhub.com
doubleverify.com
2mdn.net
Most of which are advertising sites, if rightmove use one of the same advertising sites then it's simply registered what you've been looking at and the advertising site then serves up appropriate ads on this site too.
It's no big deal, it's how the internet works, if you don't like it then the other option is you start to pay a subscription for sites like this instead of them making money from adverts.