What's the tradition behind congregational gestures during processions?

I've been going to Latin Mass on and off for a while and noticed that some people have adopted as some sort of meme a habit of bowing when the priest passes by and genuflecting when the processional cross passes by. I am personally, an obstinate stubborn sort of fool who won't adopt any practice, no matter how pious, unless it is explained to me personally. (I never dipped my hand in holy water until I heard a homily about it in my teens.) So, I'd really like to know whether or not this is a good, true and beautiful practice or just some Latin LARPer accretion which I would be best to avoid. Furthermore, if it is a good thing to do for TLM, should I do this during the *Novus Ordo* Mass? Why or why not?