I'm being a little lazy here, I should check my old lab notebook from when I TAed an analytical class; however, I believe one of the independent experiments was along the lines of a pH dependence of a commercial dye/ink. The UV spectrum would shift depending on the pH. I also think that there are dyes that are pH dependent (a quick Google search at least made me believe I am not crazy).
My guess is that the NaOH deprotonated some functionality of the dye (guessing an alcohol, maybe not though, I don't know the structure of the dye) and either reacted somehow or formed the tautomer, changing the conjugation of the dye. This tautomer could absorb a different wavelength of light, hence the color change. I guess an easy way to test this would be to take some ink, treat it with some more NaOH, then treat it with an acid. If it changes back to blue perhaps there is indeed a pH dependence. Of course if that doesn't work, maybe the NaOH just ripped apart the ink and the color change was a result of decomposition.