How is the stranger's dream ironic in Hawthorne's "The Ambitious Guest"?

The guest's dream is ironic because he states that he does not want to die until he builds his monument. Little does he know that he will soon die, and it is precisely a monument that is built as a result of his visit, although it is a monument to the deaths of the cottagers, while he is unknown. 

It is ironic, too, that the young guest who stops at the lodge naturally feels that...

The guest's dream is ironic because he states that he does not want to die until he builds his monument. Little does he know that he will soon die, and it is precisely a monument that is built as a result of his visit, although it is a monument to the deaths of the cottagers, while he is unknown. 

It is ironic, too, that the young guest who stops at the lodge naturally feels that he has ample time in order to discover himself, achieve his goals, and acquire the renown he so optimistically anticipates. At first, his guests are skeptical of his ambitions, but soon the father tells his wife that the young man's talk has made him think of things that he would like to do. Then, this ambition becomes contagious as the other family members discuss what they have dreamed of doing. And, yet the mother has a strange premonition:

"We're in a strange way, tonight," said the wife, with tears in her eyes. "They say it's a sign of something, when folks' minds go a-wandering so. Hark to the children!"

In another irony, the guest's arrival prevents the family from paying attention to the weather outside as they speak of their silent ambitions. When they finally hear the sounds of the avalanche, they rush from the cottage to their place of refuge, only to be killed. And the monument that their guest wanted constructed for himself serves instead to recall only the family.