This isn't really operating "synchronously" - you're really just trying to set up a closed-loop system. Is there an easier way? Yes. Check if the power supply has remote sense capability. This does exactly what you're trying to do. This is a far better solution that trying to perform the closed-loop system in software. In fact, I would get a different power supply if the one you have doesn't have remote sense capabilities, but that's just me.
If you *really* had to do in software you basically have to set up a while loop that get the measurements from the multimeter, compares it to the desired setting, sees if it's within your desired "error", calculates how much delta to apply to the programmed voltage for the power supply (taking into account that the
programming resolution of the power supply won't be the same as the measurement resolution of the multimeter), and the programs the power supply to the new, corrected, setting.
Still say you're better off with a power supply with remote sensing.
-Saverio