In a hennessey you can sleep allmost flat, not sure the above style will let let you.
It may prove difficult to run a tarp over the above model AND keep wind/rain out. I'd guess on that model you would just run a square tarp in half over the line that seems to be keeping the netting up (like a pup tent without ends)-provided you can keep that line taught. Run guy lines to stakes at the four corners. Similar to the "A" frame setup seen at: http://www.cloudwalkersatpage.com/page027.html
The sides of the tarp shouldn't touch the sleeping area, or condensation (from inside the tarp) could run in/puddle. To keep water from running into the hammock area along the main hammock lines, there are a few tricks. For example you can tie slip knots, leaving a few inches of cord dangling (anything that will allow water to find the easiest route down).