I am not a regular Mango user, but given the thousands of datasets that have been processed with dcm2niix I would be very surprised if it is making errors with spatial transforms. The explanation for this difference for many tools such as Slicer is that DICOM and NIfTI report the polarity of the X dimension oppositely: for DICOM X increases as you move left and with NIfTI it increases as you move right
https://www.nitrc.org/plugins/mwiki/inde...
You can easily check this by opening up your DICOM data with a dedicated DICOM viewer like Osirix: find a feature that appears on the left side of the participant. Next, load the NIfTI image with a tool that reads the NIfTI spatial transforms like MRIcroGL. Make sure to check whether the tool views in neurological or radiological convention (with MRIcroGL, you can use the Display/Radiological menu item to choose between these) - https://www.nitrc.org/plugins/mwiki/index.php/mricrogl:MainPage#Neurological_versus_radiological_convention

The feature on the patients left should remain on the patients left. If this is not the case, please file a bug report on the dcm2niix github web page. If things work out, you may want to check the Mango documentation and ask them to explicitly state how coordinates are shown from these different sources.