An ad on a news feed on the other hand is almost always something you don't want. The same goes for most ads on websites, they're likely something you do not want or something that does not align with your intend.
Seems reasonable to drive user to your site through SEM/SEO, then hammer home the message with one of these new FB add.
Early this year, I bought a watch for my girlfriend as a surprise gift for our anniversary. I made the mistake of doing some prior research to find the best price... on her laptop! I bought the watch online, using the same computer, but the advertising software was incapable of recognizing this action and kept showing her exactly the same watch ads all over the Internet. Long story short, my gift was not a surprise anymore.
That happens to me all the time, I always look the best deal before buying something online, buy it, but then have to deal with ads that are not of my interest anymore for about an extra week. I guess is more cost effective for advertisers to show completely irrelevant ads even if the purchase already materialized, but it gets so annoying to the point of starting to dislike the brand a little bit more every time. At least in my case.
Doing research to find the best price is never mistake. It sucks that your surprise is ruined. I dont know if advertisers can know if action is taken on other website. I guess you should delete cookies to "reset intent" or do research in private tab.