As stated, coaxial lighting suceeds where other lighting techniques fail due to its ability to direct subject illumination along the imaging lens axis.
However, since the most effective light source used with this technique is intense and diffuse, its very nature tends to result in a scattered dispersion pattern. The secret to acceptable photographic results is to control the distribution of the scattered light.
The diagram below illustrates the light path required for successful illumination of a subject with coaxial light.

The following diagram illustrates the the light path required for successful illumination of a subject with coaxial light, with an overlay of the "output area" of the prism assembly which is prone to the spillage of stray, non-coaxial illumination.
This diagram is not to scale, but demonstrates that an area directly below the prism's bottom surface is subject to a combination of coaxial and scattered light, and should be avoided when illuminating subject matter.

The simplest method of setting up the prism assembly would be to elevate it 1 - 2 inches (2.5 - 5 cm) above the subject by placing it on small blocks or even books.