There is no opportunity to respond between the damage being dealt and the loss of Imperishable. Immediately after this spell resolves, if the damage to a J-ruler was lethal, the J-Ruler will become Astral as a rules process before it can gain Imperishable by any other spell or ability. Similarly, if a resonator would be destroyed, it is removed from the game as a rules process immediately post-resolution of Burn to Cinders.