A useful background in the mathematics of the field being visualised would be helpful.
Of course, there would not be much maths background required for producing visual representation of the personnel organisation of a company.
I think visualisation is not a specific field.
I have done visualisation of statistical representation of data. I did not do the visualisation but I merely had the statistics background. The companies I worked for had SAS licences and I merely used the visualisation tools of SAS and then interfaced them to Tomcat/JEE.
I have had colleagues who did visualisation of manufacturing/business data using commercially licensed multi-dimensional package. I doubt they applied any mathematical knowledge but common sense.
I have seen churches visualising the data of their "faith pledge" monies using a large thermometer placed on the front lawn of their churches.
So what are you visualising? What are the avenues of display - on the LCD billboards of Times Square or Piccadilly Circus? Which end of food-cycle do you prefer to be at - the data-analyst who merely uses tools and APIs or among those writing the low level bit manipulation routines?
How about visualising geographic or astrophysics information? Assign colourisation to temperature profiles of the Universe perspectives or oceans.
Place the number of whale icons on a global map of whale population - that's easy not much of maths required but by just being a biologist in the Oceanic Administration who happens to enjoy programming. Or number of tigers, or number pandas.
How about visualising molecular structures of medicines, vaccines, viruses, or any microbiology structures. I think that you would need to get a degree first in mathematics or elec/mech/struc/chem engineering and then a masters in bioinformatics/biomedical engineering.
How about visualising structural integrity of bridges and structures? That's a job for a programmer with qualification in structural engineering.
How about visualising flow and flux and their various derivatives of electromagnetic fields but you first have to have the electrical engineering qualification to know what that means.
How about visualising fractals and bifurcation effects - that's the field of chaos.
Or making visual presentation on numeric progressions or groups - that's mathematical fields number theory and topology respectively.
I think, except for low level tools programmers, data visualisation is not a profession but a requirement of whichever field/business you are involved in. In many cases where the tool or API does not already exist, a healthy knowledge gained from a basic computer science degree of mathematical lists, maps and matrices, their transformation, translation, inversion, and other manipulation would be rather helpful to build the tool first.