There wasn't anything instant about the death, from Wikipedia:[1]
Despite intensive medical care and offers from numerous volunteers to donate blood for transfusions, Slotin's condition was incurable.[2] He called his parents and they were flown at Army expense from Winnipeg to be with him. They arrived on the fourth day after the incident, and by the fifth day his condition started to deteriorate rapidly.
Over the next four days, Slotin suffered an "agonizing sequence of radiation-induced traumas", including severe diarrhea, reduced urine output, swollen hands, erythema, "massive blisters on his hands and forearms", intestinal paralysis and gangrene. He had internal radiation burns throughout his body, which one medical expert described as a "three-dimensional sunburn." By the seventh day, he was experiencing periods of "mental confusion." His lips turned blue and he was put in an oxygen tent. He ultimately experienced "a total disintegration of bodily functions" and slipped into a coma. Slotin died at 11 a.m. on 30 May, in the presence of his parents.
[1] https://en.wikipedia.org/wiki/Louis_Slotin#Slotin's_death