The thing to keep in mind when using spherical coordinates in the VectorCalculus packages is that the names of the variables are irrelevant. It's their position in the triple spherical[u,v,w] that determines the definitions of the variables. The first name in the triple is the radial variable; the second, the angle down from the z-axis; and the third, the angle around the z-azis.
Calling the middle variable "theta" as you have done with the command SetCoordinates('spherical'[r, theta, phi]), changes the name of the "dropping down" angle to theta, but doesn't make theta match the very first image in your post.
One of the benefits of using the Student VectorCalculus package is that for Cartesian, polar, cylindrical, and spherical systems, there are default coordinate variable names recognized. For spherical, it's [r, phi, theta], with phi, being the middle name, the angle down from the z-axis, as in the diagram in your post. Your figure follows the definition of spherical coordinates found in most math books. Physics and engineering texts tend to interchange the names of the two angles. Thus, they make theta the angle down from the z-axis, and phi the angle around the z-axis.
So, the engineer of physicist using the VectorCalculus package would define a vector field in spherical coordinates with the syntax
This overwrites the defaults in the Student package and precludes the need for SetCoordinates in the VectorCalculus package.