A straight edge across the frets tells you if the frets are level, not necessarily the neck - a notched straight edge will show if it's the neck.
A rocking motion can be caused by back bow or high or low frets, but yes sounds like you have back bow to a degree
You need to loosen the truss rod a tad ; from the nut looking towards the bridge turn the truss rod Anti clockwise by a small amount, this will loosen the rod a bit.
The rod has the most effect in the centre section of the neck, - give it a try and see how you go, go 1/4vturn at a time and you will be fine, even if you get it wrong, then just go back