: loud, excited, and emotional

: involving a lot of violence, confusion, or disorder

http://www.merriam-webster.com/dictionary/tumultuously
The Story of an Hour Paragraph 10
“Now her bosom rose and fell tumultuously. She was beginning to recognize this thing that was approaching to possess her, and she was striving to beat it back with her will–as powerless as her two white slender hands would have been.”

I understand the tumultuous means that when she found out her husband died, she locked herself in the room, she was breathing with confusion, and excitement. She was crying because her husband did die, but also confused because she was excited at the thought of her freedom.