In the movie Terminator Genisys, we learn at the start how the time machine works. Specifically, one of the humans explains its limitations:
Kyle Reese: No weapons?
Female soldier: We've measured the magnetic field. It'll rip apart anything not encased in living tissue. Think "tin foil in a microwave." Times a few billion. Nothing left but a crater. Oh, no clothes, either.
Later on, we see
John Connor, infected by the machines to become one of them, gets torn to pieces in the incomplete time machine and causes a massive explosion.
Based on what we know in-movie, the time machine's field cannot touch anything that is not living tissue: even clothing which is dead tissue (e.g. cotton) would not be good. So far so good.
This explanation also agrees with the results of the final usage of the time machine, operational or not.
However, it is unclear why non-living tissue would cause such a violent reaction.
If it is due to a strong magnetic field, said field would easily penetrate living tissue and interact with the metal of terminators that use the time machine. Other terminators sent back in time would also have caused catastrophic failures.
If it is due to some other form of electromagnetic radiation, it would likely also cook living tissue (e.g. Kyle Reese) if strong enough to cause an explosion with exposed metal.
Is there any in-universe explanation from any of the Terminator movies regarding why metal would cause a time machine to explode?