I'm not sure that the errors you're providing match the source you're showing, since the undefined reference for the constructor signature has no relationship to the way you've invoked the constructor in your example.
Anyway, I suspect your problem is that order matters on the link line. The linker only walks through its libraries etc. one time, so if something that comes LATER on the link line needs something that comes EARLIER on the link line, you fail. You must order your link line such that things that require other things come first, and things that are required come later.
A few other tips: the -L option only gives search paths for libraries, so you don't need -Lsrc here as there's no library you're linking from the src directory. Also you don't need to add -L/usr/lib (in fact, it's a very bad idea) as the compiler already searches the system directories in the proper order, and on many systems (that support multiple architectures for example) /usr/lib won't be the right place.
Finally, when writing makefiles always remember that the recipe should create the exact filename of the target: for GNU make you can use $@ for that in all cases. And you need to use the source file as a prerequisite, otherwise you might as well not bother using make and just write a shell script. Try this:
NETCDF = -lnetcdf_c++
WILXAPP = src/wilxtest.cpp
CXX = g++
CXXFLAGS = -Wall -ggdb
bin/Debug/WilxAstakTest: $(WILXAPP)
$(CXX) $(CXXFLAGS) -o $@ $^ $(NETCDF)