“That is kind of weird,” she laughed. “I’m still not so sure this isn’t just coincidence. I don’t think Facebook is really listening to our conversations.” This is a terrible article. There's an easy way to figure out if it's a coincidence... repeat the experiment.
Example: my girlfriend was given a box of Flonase by her parents and immediately got a Facebook ad for it. She had not mentioned Flonase anywhere on Facebook ever. Spoopy eavesdropping? No --- she did talk on Facebook about her ENT appointment that morning. And what products might be relevant for someone going to an ENT doctor? Allergy medication.
And in cases like that, it's very likely that your two recommendations from different sources will happen to match --- what brand of medication are your parents likely to recommend? A popular one that spends a lot of $ on advertising. What brand is likely to buy ads? A popular one that spends a lot of $ on advertising.