I wanted to ask please, does a voltmeter know what is the + and what is the - of the DUT by sensing the direction of the current which flows through it when connected in parallel with the DUT?
It simply senses the polarity of the voltage, not the current. It likely senses whether the input is positive or negative with respect to the common lead with a comparator and adjusts the input polarity to the voltmeter circuit so it measures the voltage properly.