Poulin was selected by the
Sherbrooke Phoenix of the
Quebec Major Junior Hockey League (QMJHL) in the 2017 QMJHL Draft. Poulin was drafted 21st overall by the
Pittsburgh Penguins in the first round of the
2019 NHL entry draft. He signed a three-year, entry-level contract with the Penguins on September 22, 2019. Poulin served as Sherbrooke's
captain during his final two seasons with the team from 2019 to 2021. In January 2021, Sherbrooke traded Poulin to the
Val-d'Or Foreurs. Poulin made his professional debut for the
Wilkes-Barre/Scranton Penguins of the
American Hockey League (AHL) in the
2021–22 AHL season. On October 25, 2022, Poulin made his NHL debut; he recorded one assist for his first career NHL point in a 4–1 loss to the
Calgary Flames. Poulin took a leave of absence from Wilkes-Barre/Scranton in December 2022 to address
mental health concerns after suffering a
panic attack during a game. He returned to Wilkes-Barre/Scranton in March 2023. He sustained a separate lower-body injury on February 3, and returned to the lineup on March 1. On April 29, 2024, Pittsburgh re-signed Poulin to a two-year contract extension.
Edmonton Oilers On December 12, 2025, Pittsburgh traded Poulin and goaltender
Tristan Jarry to the
Edmonton Oilers in exchange for goaltender
Stuart Skinner, defenceman
Brett Kulak, and a 2029 second-round draft pick. ==International play==