I noticed that too in the blog photos. I have always understood that the idea for both pullovers and chest work was to keep your back as close to the bench as possible. I think about it whilst doing these exercises. It helps to focus the movement on the targeted muscle groups if you can not let either the back do the lifting on either standing or prone exercises.
As far as working up to a heavier weight is concerned, I find slowing the move down helps, as on S&H. Take an 8 count (play around with both 4 down and 4 counts up and a 2 counts down, 6 counts up patterns) and focus on every arc of the dumbell's movement. This will improve your strength by eliminating some of the momentum. When tarting with a new weight, it helps to lift it, makes it easier, if you hold the dumbell vertically, both hands together. As you get stronger, change your hold to a horizontal one, one hand on each end of the dumbell.
Using a dumbell for pullovers is easier again that using the barbell. The more extended weight of the barbell can make balancing the weight and controlling it more difficult. But you can graduate up to the barbell as you get stronger.
Clare