Azo compounds may typically be colorless, but in this case the azo group, and probably the sulfate group, is conjugated to the aryl pi system. This narrows the benzyl pi-pi* energy gap, which pushes it closer to the visible region. More importantly, unlike, say, a vinyl substituent, the nitrogens that make up the azo group introduce non-bonding orbitals into the electronic system. This gives rise to very low-lying n->pi* transitions, which although weakly absorbing certainly extend into to visible region. These states could also be accessed with higher energy excitation through internal conversion of the coupled vibronic states.
Photochemistry following excitation of conjugated systems is usually complicated and discerning mechanisms via inspection can be difficult. Some insight can usually be gained by trying to figuring out where electron density lies in the photoexcited molecule. Excitation of n-pi* transitions (or relaxation to n-pi* states after excitation of higher lying states) undoubtedly creates a highly polarized system where electrons are shifted from the nonbonding nitrogen orbitals into the aryl-centric pi-system. Even so, some positions on the benzyl ring will probably be more electron dense than others, so theoretical treatments may help to understand where electron rich or deficient nuclei are, which can provide a window into what's going on with the photochemistry. As a first step, you may do some reading on the photoisomerization of the related model compound azobenzene, which I understand is still a matter of some debate.https://en.wikipedia.org/wiki/Azobenzene
Keep in mind that the production of nitrogen gas in the reaction provides a thermodynamic driving force for photodissociation, as does the relatively weak N-S single bond. The n-->pi* states also hang around quite a bit longer than pi-->pi* states because their relaxation to the ground is symmetry forbidden (this is also why they absorption is weak). Meaning, there is more opportunity for photochemistry than in exclusively pi-pi* systems, where relaxation is orders of magnitude faster.
Hope that helps.