Hi @ande2
NO, you do not need Adobe Target implemented on your previous page ( for ex. facebook.com as you mentioned)
Basically, when a visitor clicks on a link from a site like facebook.com and lands on your actual site (where Adobe target implemented) the browser sends the URL of the referring page in the HTTP "referrer" header.
So when you're creating an audience in Adobe Target, you can use the "Previous Page" condition from the "Site Pages" audience category. This condition essentially checks if document.referrer matches the criteria you've added.
Just to inform referrer works only when the protocol matches like for Ex. if the previous page is https://abc then your landing page must be in https:// only.
Hope this helps.