As has been said, Tableau is fundamentally not a mapping program, although it seems the user base keeps clamoring for more mapping if not GIS functionality. It looks like the distribution in your example is perhaps based on the z-scores of the distribution of median income but I'm not sure that is in the data documentation. You are, I'm pretty sure, not missing anything in assuming that it can't be changed to something like equal intervals, equal cases, or some other custom set of breaks. If you had your own median income (not the built in values) you could use "stepped colors" for X number of steps of your choosing and set the center value of your choice in the advanced setting when editing colors on the color shelf for circle colors on a symbol map. But you would have to back out the break values for each color through some other charting. It would nice to have those as a sort of legend for color shelf steps.
Sorry I can't be of any more help!