Joseph grew up in the village of Vieille Case in Dominica. Her mother was a nurse and her father worked a variety of jobs. She graduated in 2012 with a BSc in Chemistry and mathematics from the University of the West Indies. This was followed by an MPhil in Chemistry at the same institution, graduating in 2014. She subsequently graduated with a DPhil in Chemistry from the University of Cambridge in 2018. She subsequently continued her work at Cambridge in a post-doctoral role in the team of Rosana Collepardo-Guevara. In January 2023 she was appointed Assistant Professor of Chemical and Biological Engineering at Princeton University. She works on the development of computational approaches to determine cellular organisation, in particular liquid–liquid phase separation. 
Joseph is the founder of CariScholar, an organisation designed to connect students and academics from the Caribbean for mentoring. Mentors include pscyhopharmocologist Kito Barrow, physician Mondel George, engineer Asher Williams, machine learning scientist Randall Martyr, amongst others.