One thing that seems to be clear is that HgMn stars have only an extremely weak net longitudinal magnetic field component, if any. Shorlin et al. (2002) did an early survey of HgMn, Am, and Ap stars, and detected no longitudinal magnetic fields in the former, with a median 1$\sigma$ uncertainty of 39 Gauss. Makaganiuk et al. (2010) also found $B_z$ values of 0 in the stars they surveyed, with a higher precision - a 1$\sigma$ uncertainty of 0.81-10 Gauss, varying between stars. Other studies also yielded precisions of less than a few Gauss for some stars (see mentions by Makaguniak (2011)).
Some reports have found longitudinal values in the 10s to 100s of Gauss, but as Kochukhov notes, subsequent inveistigations have failed to confirm these findings, which have had extremely high uncertainties. One example is Hubrig et al. (2012), the paper you cite, which claimed to have found weak longitudinal and quadratic fields in several stars, including HD 65949. Kochukhov et al. (2013) then found no longitudinal fields on the star, to within a few Gauss, and Bagnulo et al. (2013) attributed to 2012 findings to instrument error, leading to flawed data.
Non-longitudinal magnetic fields have not been observed in much detail (small-scale longitudinal fields have not yet been ruled out, either, by large-scale global ones appear to be nonexistent), and complicated ones could still exist. Kochukhov et al. (2013) do say that they have ruled out large so-called tangled magnetic fields, but small-scaled ones are still possible, according to Hubrig.
One thing worth noting is that the vast majority of these studies, including the one you referenced, which has been disputed, are focused on B-type HgMn stars, in part because fewer A-type HgMn stars have been discovered.