I'm unclear on exactly what keeping "shoulders down and back means". Does "down" mean extending your chest such that the shoulders stay back in position? And back meaning simply don't shrug them up but keep them down?
"Down and Back"
This is a common cue meant to tell the lifter to keep their shoulders locked into position so that the shoulder girdle remains open throughout the lift (to avoid impinging any tissues).
An easy way to feel this while standing or sitting is to raise your arms so that both your upper and lower (forearm) arm are parallel to the ground. Now pull your elbows back until you feel your upper back pinch together. While keeping this position, rotate and pull your elbows down. You should feel a small stretch in your traps when you do this.
This is the position you want your shoulder blades to remain in while pressing the barbell. I'd recommend practicing holding this position with the empty bar until you're confident that you can hold it with larger weights.