No, they don't.

Op said he visited a website that sold bicycles. If this website has a "Like" button or such a tracking pixel or Facebook analytics (do they have that?), Facebook would then know that OP is interested in this bike.

An effective ad network would know that OP already bought such a bike, so it's actually useless to try to sell him bikes... maybe accessories.

Looks like they don't! Must be a different retargeting technique used by Amazon. FB Pixel could have also been on manufacturer's site.