@acer Thanks for your comments. Yes, I can definitely obtain cartesian coordinate display of the arrows while using spherical coordinate representation for the vector-field just as you have shown. It is basically what I want. But I also need to plot the field in spherical coordinates. And the problem is that different definitions of spherical coordinates are used for these two things. I have to define my fields differently, therefore, either for cartesian or for spherical plotting. This is messy and inconvinient.
The approach suggested by @tomleslie based on Addcoordinates and MapToBasis allows me to work around this inconvinience by defining my own coordinates and sticking to them throughout all computations and visualizations. So the problem seems to be solved for me.
However different outputs of:
PlotVector(VectorField(<0, 1, 0>, spherical[r, phi, theta]), r = 0 .. 1, phi = 0 .. 2*Pi, theta = 0 .. Pi, grid = [5, 15, 5], color = black)
VectorField(<0, 1, 0>, spherical[r, phi, theta], output = plot, fieldoptions = [grid = [8, 8, 3]], color = black)
do look like a bug that needs to be taken care of by the developers..