There is a step from "DNA mutation" to "Evolution", and that is adaptation to the medium. Did the mutations change the fenotype (the external aspect/behaviour) to something more adapted? Were set certains goals (for example, putting them in a medium less than ideal for the original strain, but to which its survivors have adapted) or the surviving changes did not affect at all at the species?
I think what you're trying to ask is: "Was the selective pressure determined to be in response to stimuli versus a random occurance?"
The authors cover the difference between neutral drift and selective mutations which increase fitness throughout the paper.
Specifically in answer to your question, though, is the following from the expanded methods & materials:
"We performed Luria–Delbrück fluctuation tests33 to confirm that the Ara-1 population evolved an elevated mutation rate. Bacteria were revived from frozen stocks by growth overnight in LB medium. After dilution and 24 h of re-growth in Davis minimal medium supplemented with 25 mg l-1 glucose, we inoculated 24 replicate 10-ml cultures of Davis minimal medium with 250 mg l-1 glucose with 100–1,000 cells. After 24 h of growth to stationary phase, these cultures were concentrated by centrifugation and plated on LB agar containing 20 mug ml-1 nalidixic acid."