There is only one definite instance when a white under base is printed and that's when the graphic itself includes the color white in the design.
The other general rule is that anytime the color being printed is lighter than the shirt it is being printed on a white base would need to be laid on first. But once again this is a general rule and not always the case. Our graphics team determines whether or not an underbase is needed to make the printed result look its best. This is largely based on the artwork itself and the garment color.