Cernak, a defenseman from Kosice, Slovakia, attracted the attention of NHL scouts in his first full pro season with his hometown team in the country's top pro league. The Los Angeles Kings selected him in the second round (No. 43) of the 2015 NHL Draft.

After being drafted, Cernak opted to come to North America, playing two seasons with Erie of the Ontario Hockey League. But before his second season in Erie ended, he was traded to the Tampa Bay Lightning on Feb. 26, 2017.

Cernak played all of the 2017-18 season with Syracuse of the American Hockey League. He was sent to Syracuse after training camp in 2018, but after scoring two goals and seven points in nine games, the Lightning brought him to Tampa Bay, and he made his NHL debut against the Buffalo Sabres on Dec.. 3, 2018.

He got his first point, an assist, six nights later against the Nashville Predators, scored his first NHL goal against the New York Rangers on Feb. 2, 2019, and finished with 16 points (five goals, 11 assists) in 58 games.

Cernak was a regular on the Lightning defense in 2019-20, finishing with 12 points (five goals, seven assists) in 67 games. He also had four assists in 25 postseason games to help the Lightning win the Stanley Cup for the second time since entering the NHL in 1992. He became a two-time champion in 2021 and helped Tampa Bay to their third consecutive Stanley Cup Final in 2022, a six-game loss to the Colorado Avalanche.

He signed an eight-year contract with the Lightning on July 13, 2022 and was named to Team Slovakia's roster for the Olympic Winter Games Milano Cortina 2026.