Here is the datasheet for the voltage regulator: http://www.ti.com/lit/ds/symlink/lm2596.pdf
Keep in mind that this regulator comes in either various fixed voltage output or an adjustable voltage output. The ebay module you linked too is of course the adjustable version and uses that multiturn pot to set the output voltage. The bottom example in figure 8 shows the adjustable version and the calculation needed for the external voltage divider resistors (in your case one fixed R1, and one adjustable R2). The current requirement to drive the feedback input pins is quite low so that is not a problem, but trying to replace the R2 component with a digital pot IC may run into a voltage limit size as the digital pot would have to be rated to handle the maximum rated output voltage you plan on running the regulator at. Using an arduino to read the output voltage of the module and apply a nominal (but adjustable) 1.23 adjustable voltage (say from a low pass filtered PWM output pin) to the regulator feedback pin might work in theory but I think you would have problems with the low resolution of the standard arduino PWM command (only 256 step values and only a few counts would be in the 'control range' of the module as there is most likely a high 'gain factor'. Also timing might be critical.
So not saying it can't be done (arduino controlling output voltage value of this regulator) but it would be a project for someone with good experience in electronics. Perhaps an arduino controled 'motorized pot' as used in stereo equipment could be used with the motorized pot replacing the blue pot in that module? Of course the motorized pot variable resistor range would have to be of the same ohm range (and have a linear 'taper' Vs 'log taper') as the pot used in the regulator module and you probably would need a second pot 'gang' on the motorized pot to give position feedback to the arduino and of course finally you would need a motor H-drive to power the motor on the pot. Example:http://www.ebay.com/itm/ALPS-dual-motorized-rotary-Potentiometer-RK16812MG-10K-o-100K-log-o-linear-pot-/261072098091?pt=LH_DefaultDomain_0&hash=item3cc91c132b
Again not the simplest of projects to take on, put certainly could be a useful one if actually accomplishable with reasonable costs and size.