If your HV neutral is floating, then you do not have a path for the 3rd harmonic (and other harmonics) magnetising HV currents. The result is the ph to ph voltages will read ok, however the phase to neutral voltages will not read correctly as they have a 3rd harmonic & other harmonic components.
Attached is a paper which although not directly related to sympathetic inrush has a simple explanation on its cause.
The paper describes how the sympathetic inrush distorts the transformers secondary voltage and results in neutral currents which can operate sensitive earth fault protection...
