Actually the verbosity = 10 trick works also post-scf. So, you could just do
from ATK.TwoProbe import *
import ATK
scf = restoreSelfConsistentCalculation('my_ncfile.nc')
ATK.setVerbosityLevel(10)
m = calculateMullikenPopulation(scf)
The returned objects from various "calculate..." functions are often quite "thin" and don't have so many methods. The object "m" returned in the example above only has one real method, "toArray" which will return the populations per atom.
Others have a few more, and you can always see which by using the "dir()" function (like print dir(m) in the example above), or if you are running ATK interactively you can use the TAB key after writing "m." (note the ".") to expand the available methods.
In case you want the orbital-resolved populations as an array, it's more tricky.