Answer:
The way I think readers assume about a writer's real life is when they add a lot of personal emotions to their stories, Dickinson's poems were considered romantic meaning she loved someone back in the day and wrote about it in her poems. A lot of readers tend to write out their problems including love life, personal family life in books or poems to express their feelings and that is what readers assume when reading a book. Another perfect example is William Shakespeares' love sonnets and his love drama and readers/audiences realized there was something going on in his life. A lot of readers/audiences (whether it is a film or book) assume an actor or writer puts in their own personal story and have their character act it out, letting out their emotions which brings a lot of different drama, love, power, etc.
Dickinson's poems also mentioned a lot of death in her poems which makes readers think someone she once loved died and she is expressing all of the emotions she kept hidden out in her poems.
Hope this helped :)