Well that makes sense- I am new to this RV thing too. I always to dump the sewer first & then grey last like it says, but I never thought to fill it up before dumping... good stuff.
Just poo lots of times in the RV & when it is time to leave, open sewer valve & drive RV for 3 miles (go fast so you don't get splash-back on RV siding). Then open the gray water, drive for 3 more miles (make sure sewer line is rinsed good). Then close em' both & drive home. That is the safe & responsible way to do it brethren. Oh yeah-- make sure you wear clean gloves when you open/close sewer valve.