A military pilot conducting a PAR Approach reported after descending to minimum descent altitude as instructed by ATC they received a Low Altitude Alert from ATC.

Narrative

Instrument training flight conducting practice GCA's (Ground Controlled Approaches) at NIP enroute to final destination. Both instructor and student are fairly confident controller said 'descend to minimum descent altitude.' Student initiated steady slow descent as we were still probably 8 nm from the field. The controller continued to offer course guidance and then stated 'low altitude alert; check altitude immediately.' We climbed; and later heard; what we thought for a second time; 'descend to minimum descent altitude.' At that point; we thought maybe we misheard the controller the first time; or that we climbed too high to comply with previous instructions.Having heard that warning before years ago; it was usually when doing an ASR and using the dive and drive method to get to MDA. What was different this time was that we were a bit further from the field than past approaches at other locations. This time; I never got clarification whether we climbed too high in compliance with controller instructions leading him to state the instruction to descend a second time; or if we indeed descended too early and misheard. In the future; I will use a non-standard technique of crosschecking DME before accepting descent instructions on a GCA. If more than 5 DME or so; I will crosscheck another approach's FAF before beginning descent.