Born in Tesin (Silesia) on 1 January 1898, Ullmann grew up and was educated in Vienna. He participated in Schoenberg's advanced courses in 1918-19, and at Schoenberg's recommendation, became one of Alexander Zemlinsky's conducting assistants at the New German Theatre in Prague in the 1920s. How highly Zemlinsky regarded him is seen in his having entrusted Ullmann with the preparation of Schoenberg's Gurre-Lieder, as well as operas of Mozart, Strauss, Wagner, Berg and others, which he also conducted on occasion in place of Zemlinsky. During the 1927-28 season, Ullmann became First Kapellmeister at the municipal theatre in Aussig. In both cities, Ullmann enjoyed a reputation as an excellent, conscientious and capable conductor. An active member of the Schoenberg circle, Ullmann was also a devoted follower of Rudolf Steiner's anthroposophical movement. In the 1930s he composed, taught and wrote articles for German musical publications in Prague.
Following unsuccessful efforts to find work in London or South Africa, Ullmann was trapped in Prague after the German invasion in March 1939. In 1942 he was deported to Terezin. Rather exceptionally, instead of being given a customary work assignment, Ullmann was instead asked by the Freizeitgestaltung (Leisure time authority) to occupy himself with music, serving as critic and concert organiser (including the Studio for New Music, which he founded, and the Collegium Musicum) as well as assisting on other performances, lecturing on such subjects as Mahler's First Symphony, anthroposophy and music and other topics. He also had more time to compose, which accounts for his unusually prolific production in comparison to the other Terezin composers.
Besides his impressive list of original compositions – three piano sonatas, a string quartet, several dozen Lieder, orchestral works and an opera, The Emperor of Atlantis or Death Abdicates – Ullmann made, upon request, a number of vocal arrangements of Yiddish and Hebrew songs. In addition to his extensive concert reviews, he wrote several essays, an opera libretto and a literary diary, The Strange Passenger, a collection of poems and aphorisms. This latter document discloses Ullmann's deep despondency, his conflict about his Jewish identity, his basically Christian religiosity and his cynicism. Nevertheless, in a frequently-quoted essay, ‘Goethe and Ghetto’, Ullmann considers the meaning of Goethe for ‘educated Europeans’ in both daily living and culture . But where the interaction of life and art had earlier allowed the easier creation of beautiful forms, in Terezin this was difficult, ‘where anything connected with the muses is in utter contrast to the surroundings.’ Maintaining that future generations would find no interest in the lack of pianos and music paper, Ullmann concludes in a profound expression of his and his colleagues' reserves of spiritual strength:
it must be emphasised that Theresienstadt has served to enhance, not to impede, my musical activities, that by no means did we sit weeping on the banks of the waters of Babylon, and that our endeavour with respect to Arts was commensurate with our will to live. And I am convinced that all those who, in life and in art, were fighting to force form upon resisting matter, will agree with me.