The unnamed narrator in "A Rose for Emily" is a plural, first person "we" narrator--the townspeople. It's a collective or communal "we" narrator.
That's why, presumably, information comes haphazardly to the reader. It's presented in a fragmented way that mimics the way information passes through a small town. The narrator gets the information about Emily buying poison from the pharmacist, presumably. The narrator gets information about the inside of the house from someone that was in the group that visited her to try to get her to pay taxes, presumably. The narrator hears about problems updating Emily's house for modern postal delivery from someone who had to hassle with her, presumably. The narrator is the townspeople.
This, of course, is all a construct created by Faulkner to enable him to pull off the surprise ending. The plot details, told in chronological order, obviously feature Emily murdering Homer, etc. Told chronologically, the feature cannot create a surprise ending. That is only possible if the plot details are manipulated. That's the purpose the "we" narrator serves.