We compared the magnetic field directions inferred from polarimetry data obtained from 100 pc scale inter-cloud media (ICM) and from sub-parsec scale molecular cloud cores. The highly correlated result led us to conclude that cloud turbulence must be sub-Alfvénic. Here we extend the study with 0.01 pc cores observed by interferometers. The inferred field directions at this scale significantly deviate from that of the surrounding ICM. An obvious question to ask is whether this high-resolution result contradicts the sub-Alfvénic picture concluded earlier. We performed MHD simulations of a slightly super-critical clouds with Alfvénic Mach number MA=0.63 which can reproduce the Paper I result, and observed the development toward smaller scales. Interestingly, all subregions hosting cores with n(H2)>10^5/cc (the typical density observed by interferometers) possess MA=2~3. Not too surprisingly, these slightly super-Alfvénic cores result in B-field orientation offsets comparable to the interferometer observations. The result suggests that gravity can concentrate (and maybe also contribute to, which requires further study to confirm) turbulent energy and create slightly super-Alfvénic cores out of sub-Alfvénic clouds. The results of our simulations also agree with the observed velocity-scale, mass-scale, and field-density relations