2008-09: Tommernes spent 11 games with Frolunda in Sweden's Elitserien and was the second-leading scorer for Frolunda's U20 team. Tommernes had no points or penalties in his time with the Elitserien club. In 40 games for Frolunda U20 he scored 10 goals with 22 assists and 52 PMs. In five games during the SuperElit playoffs he led Frolunda with 8 points; scoring 2 goals with 6 assists. Despite his impressive numbers, Tommernes was not listed among the 30 European skaters in Central Scouting's final rankings and was not selected in the 2009 NHL Draft.
2009-10: Tommernes split his first full pro season between the Elitserien's Frolunda and Boras in AllSvenskan (Sweden's second division). In 27 games with Frolunda he had 3 assists and was +5 with 10 PMs; averaging 7:32 minutes of ice time. Tommernes' role increased in the playoffs, as he averaged over 15 minutes of ice time and he was an even plus/minus with 1 assist and 2 PMs. Seventh-place Frolunda forced Linkopings to a deciding seventh game. In 23 games with Boras Tommernes scored 5 goals with 9 assists and had 43 PMs.
2010-11: Tommernes skated in 47 games for Frolunda and was the club's leading scorer amongst defensemen in his first full Elitserien season. Tommernes scored 3 goals with 17 assists and was -17 with 24 PMs. Frolunda finished 9th in the 12-team league, one point behind AIK for the final playoff spot. The Canucks selected Tommernes as a 20-year-old with the next-to-last pick in the 2011 NHL Draft.
2011-12: Drafted by the Canucks as a 21-year-old following an impressive rookie season in Sweden's Elitserien, Tommernes saw a dip in his offensive numbers in his second year with Frolunda but was a much-improved plus-11 after finishing minus-17 in 2010-11. He scored 3 of his 5 goals on the Frolunda power play and had 9 assists with 36 penalty minutes in 44 games. Frolunda reached the playoff quarterfinals after finishing fifth during the regular season. In six playoff games Tommernes shared the points lead for the team with veteran forward Mathis Olimb; scoring 1 goal with 3 assists and finishing minus-two with 4 penalty minutes.