Lats should be the primary mover with these, and yes, doing them at a decline is a superior movement, in my opinion. It increases the range of motion, while reducing shoulder impingement.
I actually prefer doing these with cables…provides constant tension, and you don’t have to waste as much energy on stabilizing the weight. A rope, short EZ bar, or short straight bar all work well. I prefer the rope the most, as it’s easier on the wrists.
I don’t focus on “working” my chest when doing these (other than keeping a big chest at the bottom of the movement)…focus on the stretch (not maximal stretch) of the lats at the bottom of the movement (don’t come to a complete stop at the bottom of each rep, but be sure to remain “tight” at the bottom), and initiating the pull with the lats. When using cables, I like to pull each rep all the way up, until my hands are basically over my stomach (the cable provides tension throughout the whole ROM). If using a DB, I’d stop your pull when your hands are above your upper chest, otherwise you lose some tension in the lats, and if you’re arms are locked out, you’d basically be supporting the weight due to a locked elbow position.
Also, if you internally rotate your upper arms each rep as you pull the weight up, it would involve the chest a bit more, as they are internal rotators of the upper arm.
Pullovers are great for working the serratus…which may be why people confuse them with a “chest” exercise.