I often yawn after my cats do, but I haven’t noticed the reverse. They do yawn a lot in my presence though, but that’s probably because they find me boring (unless I’m eating, then they’re my biggest fans—damn cats!).
They do slow blink at me when I do so first. That’s cat/human communication, showing they are comfortable, and trust me—sweet cats!
I’m their comfortable, but boring old shoe…who they can steal food from.
That goes a long way toward explaining why they make such good service dogs - especially the kind that monitor people for subtle signs of medical distress, like incipient diabetic episodes or epileptic seizures.