When I'm printing a two color job, that is printed on yellow paper, does that mean it uses one ink color and one paper color?

The answer is, “no”.  When a printer or designer is talking about two colored jobs, they are only referring to the number of inks on the press. (Yes, black counts as a color.) If you wanted to you could print on a rainbow color piece of paper, but with two color printing you still have two colored inks to work with.