2009-10: Ullmark spent most of the season with MODO's U18 team and played in two games for Kramfors-Alliansen U18. Playing behind Elias Axelsson-Svensson, he had 1 shutout in four appearances and finished with a 3.00 goals against and .893 save percentage during the Elit league qualifiers. In Allsvenskan play, he appeared in 4 of 18 games for fifth-place MODO and had a 3.44 goals against and .894 save percentage. In the playoffs, he stopped 24 of 25 shots in a win against Kramfors-Alliansen and was in net for MODO's 6-2 loss to Timra. He finished the playoffs 1-1 with a 3.49 goals against and .850 save percentage. Ullmark allowed 11 goals on 61 shots (.820 save percentage) in two games with Kramfors.
2010-11: Ullmark made one appearance for MODO U20 and handled the bulk of the goaltending for the club's U18 squad. He allowed 2 goals on 26 shots in his only U20 game. Splitting time with Isak Edman in the U18 Elit league qualifiers, he appeared in 11 games and had 1 shutout with a 2.05 goals against and .925 save percentage (MODO U18 lost just once in 22 games in Elit play, finishing first). MODO finished fourth in Allsvenskan with Ullmark appearing in 13 of 18 games. He recorded four shutouts and had a 2.35 goals against and .913 save percentage. After receiving a first round bye, MODO lost to Skelleftea in a three-game second round playoff series. Ullmark started two of three games – getting a 5-2 win in the opener – and was 1-1 with 3.49 goals against and .850 save percentage.
2011-12: Ullmark made his men's league debut, appearing in three games in the Elitserien with MODO and was the top goalie for the club's U20 squad. He made his first pro start with MODO on December 26 in a game against Lulea and stopped 34 of 37 shots in a 3-2 overtime loss. He finished 0-2 with a 3.24 goals against and .889 save percentage in Elitserien play. Ullmark tied Lulea's Joel Lassinantti for the sixth-best save percentage (.918) in the SuperElit U20 league. In 17 regular season games he had 1 shutout with a 2.50 goals against and .918 save percentage as MODO finished third. Ullmark split time with Anton Forsberg in Top 10 play, appearing in 8 of 18 games, and had a 3.33 goals against and .918 save percentage. In the playoffs MODO faced Rogle in the bronze medal game after falling to Linkopings in the semifinal. Ullmark and Forsberg shared the goaltending duties and in five playoff games Ullmark recored 1 shutout and had a 2.24 goals against and .927 save percentage. Ullmark was ranked seventh amongst European goalies in Central Scouting's final rankings and was selected by Buffalo in the sixth round (163rd overall) of the 2012 NHL Draft.
Big, raw, but undeniably talented, Ullmark is a standout in the Swedish junior circuit. He is one of Sweden’s less heralded goaltenders and was passed over in the previous draft. He has the ability to make the NHL down the road, but he will not be a starter.
Ullmark is a long-term project and will spend as much time as he can in Sweden before heading overseas.