There are various types of irony, but the one that is mainly employed in "Tell Them Not to Kill Me!" is situational irony. Situational irony refers to when the expectations one has for a situation's outcome contrast with what actually happens. You may want to consider Juvencio's situation.

The basic premise of the story is that Juvencio has been in hiding for decades in order to escape prosecution for the murder of Don Lupe Terreros. Finally, after being caught, it is revealed that the person Juvencio must answer to for the murder of Don Lupe is none other than Don Lupe's son himself.

This is an example of irony due to Juvencio's expectations. While he was in fear of being prosecuted the entire time he was in hiding, he did not expect that the person who would bring him to justice would be the very victim's son himself.

"Tell Them Not to Kill Me!" has a few ironies. The first irony is that Juvencio Nava has to beg his son to try to intervene on his behalf to save his life, and his son does not wish to do so. It seems ironic that a son would not try to preserve his own father's life. When Juvencio's son asks who would look after his wife and children if something happened to him, Juvencio tells him that Providence will look after him. It seems, ironically, that perhaps Providence is looking after the children of Don Lupe Terreros, since Juvencio will now have to answer for his murder. And it is ironic that Don Lupe Terreros is looking after his own father, in a sense, while Juvencio's son will not.

Because Juvencio has lived for decades and eluded retribution for killing Don Lupe Terreros, it is ironic that as an old man, he is finally captured and called to answer for it by Terreros's son.