He made his American debut in 2004 as Dick Johnson in Puccini's La fanciulla del West at the Seattle Opera.
In the 2007/2008 season, he made a debut as Alvaro in La forza del destino in Monte Carlo, followed by La fanciulla del West in Rome and Norma in Bologna; in 2008/2009, he performed Tosca in Florence, Adriana Lecouvreur in Palermo and La fanciulla del West in Seville.
Although he composed the part of Minnie in La fanciulla del West for another soprano, when Puccini saw Dalla Rizza in the part, he said, "At last I have seen my true Fanciulla".
Giacomini made his North American debut as Ramerrez in La fanciulla del West in Connecticut, 1975, making his Metropolitan Opera debut the year afterwards in La forza del destino.
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At the Met he sang in the world premieres of several operas, including Giacomo Puccini's, La fanciulla del West (1910), Umberto Giordano's Madame Sans-Gêne (1915), Charles Wakefield Cadman's Shanewis (1918), Puccini's Il tabarro (1918), Puccini's Gianni Schicchi (1918), Albert Wolff's, L'oiseau bleu (1919), and Deems Taylor's Peter Ibbetson (1931).
He remained with the Met until 1914, appearing in numerous world premieres, including those of the Monk in Walter Damrosch's Cyrano, Happy in La fanciulla del West, the Innkeeper in Engelbert Humperdinck's Königskinder, and Mauprat in Victor Herbert's Madeline.
Following engagements in Nice and Brussels, she became a member of the Boston Opera Company in 1911 where her roles included Minnie in La fanciulla del West and the title role in Aida.
At the Boston Opera House he performed the roles of Alfio, Amonasro, Count di Luna, Enrico, Figaro, Germont, Jack Rance in La Fanciulla del West, Marcello, Rafaele in I gioielli della Madonna, Riccardo, Scarpia, Sharpless, and Tonio.
Outside of the mainstream, OperaUpClose has presented Puccini's La fanciulla del West directed by Robert Chevara; Benjamin Britten's The Turn Of The Screw directed by Edward Dick; and Claudio Monteverdi's The Coronation of Poppea directed by Mark Ravenhill.