Again, the order of failure is incorrect in that statement. You most likely had the tube "pinched" under the bead of the tire and upon inflation it eventually pushed the bead up out of the rim, allowing the tube to "escape containment" and subsequently pop.

Tubes are not "explosive devices". They can't spontaneously explode inside a tire and cause higher pressures than what is in there to begin with. They CAN be punctured either with an object through the tire or by not having a well installed rim tape (exposing holes in the rim for the tube to fail on), but in those cases they won't make a loud "pop" or "bang" since they are contained inside of the "pressure vessel", or tire.