Running the cords this way is the standard and should force the wire end of the plate toward the head under tension, resulting in good contact.Interesting. My regular snare was hooked up the same way. I wonder if running the strings under would affect it as well. With the flat mounting plate, it may have the effect of raising the wires off the head just a bit.
edit: In my experience, you have to experiment. Some wire sets work better with cord, some with straps. Always good to have both on hand.