The freshwater tank shouldn't fill - there's a check valve at the city water inlet connection that should prevent this. It sounds like this check valve isn't working on your trailer and needs to be replaced.
The blue and red water hoses are low point drains - mainly used when winterizing the trailer to drain out water or antifreeze. The white valve at the end of the freshwater tank is the one you want to use. You'll have to have someone stand outside and let you know when water comes out (or turn it a quarter turn, go check, turn another quarter turn, etc.. until water comes out). Even so it won't allow ALL of the water to drain from the tank, just most of it. It won't hurt anything to have that little bit left in there though.
If it's any consolation, the manual is neither better nor worse than most other brands.